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First Year Math Partial Fractions Resolve into partial fractions.6. \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}


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Resolve into partial fractions.6. \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}

Resolve into partial fractions.4. \frac{x-5}{x^{2}+2 x-3}
Resolve into partial fractions.4.  \frac{x-5}{x^{2}+2 x-3}

Resolve into partial fractions.4. \frac{x-5}{x^{2}+2 x-3}

2. Write short answers of the following questions.(viii) Resolve \frac{x}{(x-3)^{2}} into partial fractions:
2. Write short answers of the following questions.(viii) Resolve  \frac{x}{(x-3)^{2}}  into partial fractions:

2. Write short answers of the following questions.(viii) Resolve \frac{x}{(x-3)^{2}} into partial fractions:

Q.21 The rational fraction \frac{P(x)}{Q(x)} is a proper fraction if(a) Degree of P(x)= degree of Q(x) (b) Degree of P(x)< degree of Q(x) (c) Degree of Q(x)< degree of P(x) (d) none of these
Q.21 The rational fraction  \frac{P(x)}{Q(x)}  is a proper fraction if(a) Degree of  P(x)=  degree of  Q(x) (b) Degree of  P(x)<  degree of  Q(x) (c) Degree of  Q(x)<  degree of  P(x) (d) none of these

Q.21 The rational fraction \frac{P(x)}{Q(x)} is a proper fraction if(a) Degree of P(x)= degree of Q(x) (b) Degree of P(x)< degree of Q(x) (c) Degree of Q(x)< degree of P(x) (d) none of these

Q.13 The fraction \frac{x^{2}+7 x+3}{x+1} is :(a) Improper(b) Proper-(c) Equivalent(d) Identity
Q.13 The fraction  \frac{x^{2}+7 x+3}{x+1}  is :(a) Improper(b) Proper-(c) Equivalent(d) Identity

Q.13 The fraction \frac{x^{2}+7 x+3}{x+1} is :(a) Improper(b) Proper-(c) Equivalent(d) Identity

Resolve into partial fractions.5. \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}
Resolve into partial fractions.5.  \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}

Resolve into partial fractions.5. \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}

2. Write short answers of the following questions.(ii) What is a proper fraction? .
2. Write short answers of the following questions.(ii) What is a proper fraction? .

2. Write short answers of the following questions.(ii) What is a proper fraction? .

7.\[\frac{1}{(x-1)^{2}(x+1)}\]
7.\[\frac{1}{(x-1)^{2}(x+1)}\]

7.\[\frac{1}{(x-1)^{2}(x+1)}\]

6 . \[\frac{x^{2}}{(x-2)(x-1)^{2}}\]
 6 . \[\frac{x^{2}}{(x-2)(x-1)^{2}}\]

6 . \[\frac{x^{2}}{(x-2)(x-1)^{2}}\]

Q.1 A relation in which the equality is true only for a number of unknowns is called an(a) identity(b) equation(c) algebraic equation(d) algebraic relation
Q.1 A relation in which the equality is true only for a number of unknowns is called an(a) identity(b) equation(c) algebraic equation(d) algebraic relation

Q.1 A relation in which the equality is true only for a number of unknowns is called an(a) identity(b) equation(c) algebraic equation(d) algebraic relation

Q.30 Partial fractions of \frac{(x-a)(x-b)}{(x-c)(x-d)} will be of the form:(a) \frac{A}{x-c}+\frac{B}{x-d} (b) 1+\frac{A}{x-a}+\frac{B}{x-b} (c) \frac{A}{x-a}+\frac{B}{x-b} (d) 1+\frac{B}{x-c}+\frac{A}{x-d}
Q.30 Partial fractions of  \frac{(x-a)(x-b)}{(x-c)(x-d)}  will be of the form:(a)  \frac{A}{x-c}+\frac{B}{x-d} (b)  1+\frac{A}{x-a}+\frac{B}{x-b} (c)  \frac{A}{x-a}+\frac{B}{x-b} (d)  1+\frac{B}{x-c}+\frac{A}{x-d}

Q.30 Partial fractions of \frac{(x-a)(x-b)}{(x-c)(x-d)} will be of the form:(a) \frac{A}{x-c}+\frac{B}{x-d} (b) 1+\frac{A}{x-a}+\frac{B}{x-b} (c) \frac{A}{x-a}+\frac{B}{x-b} (d) 1+\frac{B}{x-c}+\frac{A}{x-d}

Resolve into partial fractions.6. \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}
Resolve into partial fractions.6.  \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}
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Resolve into partial fractions.6. \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}

Q.28 Partial fractions of \frac{7 x+25}{(x+3)(x+4)} is of the form(a) \frac{A}{x+3}+\frac{B x}{x+4} (b) \frac{A}{x+3}+\frac{B}{x+4} (c) \frac{A x+B}{x+3}+\frac{C}{x+4} (d) \frac{A x+B}{(x+3)(x+4)} Lahore Board 2014
Q.28 Partial fractions of  \frac{7 x+25}{(x+3)(x+4)}  is of the form(a)  \frac{A}{x+3}+\frac{B x}{x+4} (b)  \frac{A}{x+3}+\frac{B}{x+4} (c)  \frac{A x+B}{x+3}+\frac{C}{x+4} (d)  \frac{A x+B}{(x+3)(x+4)} Lahore Board 2014

Q.28 Partial fractions of \frac{7 x+25}{(x+3)(x+4)} is of the form(a) \frac{A}{x+3}+\frac{B x}{x+4} (b) \frac{A}{x+3}+\frac{B}{x+4} (c) \frac{A x+B}{x+3}+\frac{C}{x+4} (d) \frac{A x+B}{(x+3)(x+4)} Lahore Board 2014

Resolve into partial fractions.3. \frac{9}{(x-1)(x+2)^{2}}
Resolve into partial fractions.3.  \frac{9}{(x-1)(x+2)^{2}}

Resolve into partial fractions.3. \frac{9}{(x-1)(x+2)^{2}}

Resolve into partial fractions.5. \frac{7 x+4}{(3 x+2)(x+1)^{2}}
Resolve into partial fractions.5.  \frac{7 x+4}{(3 x+2)(x+1)^{2}}

Resolve into partial fractions.5. \frac{7 x+4}{(3 x+2)(x+1)^{2}}

5. \frac{x^{2}}{\left(x^{2}+4\right)(x+2)}
5.  \frac{x^{2}}{\left(x^{2}+4\right)(x+2)}

5. \frac{x^{2}}{\left(x^{2}+4\right)(x+2)}

Resolve into partial fractions.5. \frac{x^{4}}{\left(x^{2}+2\right)^{2}}
Resolve into partial fractions.5.  \frac{x^{4}}{\left(x^{2}+2\right)^{2}}

Resolve into partial fractions.5. \frac{x^{4}}{\left(x^{2}+2\right)^{2}}

Q.6 (x-4)^{2}=x^{2}-8 x+16 is(a) a transcendental equation(b) cubic equation(c) an identity(d) an equation
Q.6  (x-4)^{2}=x^{2}-8 x+16  is(a) a transcendental equation(b) cubic equation(c) an identity(d) an equation

Q.6 (x-4)^{2}=x^{2}-8 x+16 is(a) a transcendental equation(b) cubic equation(c) an identity(d) an equation

Example 1: Resolve the fraction \frac{x^{3}-x^{2}+x+1}{x^{2}+5} into proper fraction.
Example 1: Resolve the fraction  \frac{x^{3}-x^{2}+x+1}{x^{2}+5}  into proper fraction.

Example 1: Resolve the fraction \frac{x^{3}-x^{2}+x+1}{x^{2}+5} into proper fraction.

9. \frac{x^{4}}{1-x^{4}}
9.  \frac{x^{4}}{1-x^{4}}
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9. \frac{x^{4}}{1-x^{4}}

Q.17 An improper fraction can be reduced to proper fraction by : (a) addition(b) subtràction (c) multiplication(d) division Lahore Board 2015; Multàn Boảrd 2004)
Q.17 An improper fraction can be reduced to proper fraction by : (a) addition(b) subtràction (c) multiplication(d) division Lahore Board 2015; Multàn Boảrd 2004)
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Q.17 An improper fraction can be reduced to proper fraction by : (a) addition(b) subtràction (c) multiplication(d) division Lahore Board 2015; Multàn Boảrd 2004)

Q.35 The fraction \frac{3}{x+1} is(b) improper fraction(a) proper fraction(d) irrational fraction
Q.35 The fraction  \frac{3}{x+1}  is(b) improper fraction(a) proper fraction(d) irrational fraction
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Q.35 The fraction \frac{3}{x+1} is(b) improper fraction(a) proper fraction(d) irrational fraction

(vi) (x+3)^{2}=x^{2}+6 x+9 is(a) a linear equation(b) an equation(c) an identity(d) none of these
(vi)  (x+3)^{2}=x^{2}+6 x+9  is(a) a linear equation(b) an equation(c) an identity(d) none of these
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(vi) (x+3)^{2}=x^{2}+6 x+9 is(a) a linear equation(b) an equation(c) an identity(d) none of these

Q.27 Partial fractions of \frac{7 x^{2}+25}{(x+3)(x+4)} will be of the form(a) \frac{A}{x+3}+\frac{B}{x+4} (b) 1+\frac{A}{x+3}+\frac{B}{x+4} (c) 7+\frac{A}{x+3}+\frac{B}{x+4} (d) none of these
Q.27 Partial fractions of  \frac{7 x^{2}+25}{(x+3)(x+4)}  will be of the form(a)  \frac{A}{x+3}+\frac{B}{x+4} (b)  1+\frac{A}{x+3}+\frac{B}{x+4} (c)  7+\frac{A}{x+3}+\frac{B}{x+4} (d) none of these
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Q.27 Partial fractions of \frac{7 x^{2}+25}{(x+3)(x+4)} will be of the form(a) \frac{A}{x+3}+\frac{B}{x+4} (b) 1+\frac{A}{x+3}+\frac{B}{x+4} (c) 7+\frac{A}{x+3}+\frac{B}{x+4} (d) none of these

2. Write short answers of the following questions.(i) Define a rational fraction.
2. Write short answers of the following questions.(i) Define a rational fraction.
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2. Write short answers of the following questions.(i) Define a rational fraction.

2. Write short answers of the following questions.(iv) What are partial fractions?
2. Write short answers of the following questions.(iv) What are partial fractions?
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2. Write short answers of the following questions.(iv) What are partial fractions?

Q.31 The partial fractions of \frac{9 x-7}{\left(x^{2}+1\right)(x+3)} are of the form:(a) \frac{A x+B}{x^{2}+1}+\frac{C}{x+3} (b) \frac{A}{x^{2}+1}+\frac{B}{x+3} (c) \frac{A}{x^{2}+1} (d) \frac{B}{x+3}
Q.31 The partial fractions of  \frac{9 x-7}{\left(x^{2}+1\right)(x+3)}  are of the form:(a)  \frac{A x+B}{x^{2}+1}+\frac{C}{x+3} (b)  \frac{A}{x^{2}+1}+\frac{B}{x+3} (c)  \frac{A}{x^{2}+1} (d)  \frac{B}{x+3}
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Q.31 The partial fractions of \frac{9 x-7}{\left(x^{2}+1\right)(x+3)} are of the form:(a) \frac{A x+B}{x^{2}+1}+\frac{C}{x+3} (b) \frac{A}{x^{2}+1}+\frac{B}{x+3} (c) \frac{A}{x^{2}+1} (d) \frac{B}{x+3}

6. \frac{x^{2}+1}{x^{3}+1}
6.  \frac{x^{2}+1}{x^{3}+1}
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6. \frac{x^{2}+1}{x^{3}+1}

Resolve into partial fractions.5. \frac{3 x+3}{(x-1)(x+2)}
Resolve into partial fractions.5.  \frac{3 x+3}{(x-1)(x+2)}
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Resolve into partial fractions.5. \frac{3 x+3}{(x-1)(x+2)}

8. \frac{1}{(x-1)^{2}\left(x^{2}+2\right)}
8.  \frac{1}{(x-1)^{2}\left(x^{2}+2\right)}
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8. \frac{1}{(x-1)^{2}\left(x^{2}+2\right)}

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