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Class 9 Math Algebric Expressions and Algebric Formulas 3. Reduce the following rational expresions to the lowest form.(i) \frac{120 x^{2} y^{3} z^{5}}{30 x^{3} y z^{2}}


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3. Reduce the following rational expresions to the lowest form.(i) \frac{120 x^{2} y^{3} z^{5}}{30 x^{3} y z^{2}}

6. Perform the indicated operation and simplify.(i) \left(x^{2}-49\right) \cdot \frac{5 x+2}{x+7}
6. Perform the indicated operation and simplify.(i)  \left(x^{2}-49\right) \cdot \frac{5 x+2}{x+7}

6. Perform the indicated operation and simplify.(i) \left(x^{2}-49\right) \cdot \frac{5 x+2}{x+7}

4. If x^{2}+y^{2}+z^{2}=78 and x y+y z+z x=59 then find the value \delta f x+y+z .
4. If  x^{2}+y^{2}+z^{2}=78  and  x y+y z+z x=59  then find the value  \delta f x+y+z .

4. If x^{2}+y^{2}+z^{2}=78 and x y+y z+z x=59 then find the value \delta f x+y+z .

2. Find the conjugate of x+\sqrt{y} .(v) 5+\sqrt{7}
2. Find the conjugate of  x+\sqrt{y} .(v)  5+\sqrt{7}

2. Find the conjugate of x+\sqrt{y} .(v) 5+\sqrt{7}

1. Rationalize the denominator of the following.(vi) \frac{2}{\sqrt{5}-\sqrt{3}}
1. Rationalize the denominator of the following.(vi)  \frac{2}{\sqrt{5}-\sqrt{3}}

1. Rationalize the denominator of the following.(vi) \frac{2}{\sqrt{5}-\sqrt{3}}

Example 3If a+b+c=7 and a b+b c+c a=9 then find the value of a^{2}+b^{2}+c^{2} .
Example 3If  a+b+c=7  and  a b+b c+c a=9  then find the value of  a^{2}+b^{2}+c^{2} .

Example 3If a+b+c=7 and a b+b c+c a=9 then find the value of a^{2}+b^{2}+c^{2} .

2. Find the conjugate of x+\sqrt{y} .(i) 3+\sqrt{7}
2. Find the conjugate of  x+\sqrt{y} .(i)  3+\sqrt{7}

2. Find the conjugate of x+\sqrt{y} .(i) 3+\sqrt{7}

(iv) (3+\sqrt{2})(3-\sqrt{2}) is equal to(a) 7(b) -7 (c) -1
(iv)  (3+\sqrt{2})(3-\sqrt{2})  is equal to(a) 7(b)  -7 (c)  -1

(iv) (3+\sqrt{2})(3-\sqrt{2}) is equal to(a) 7(b) -7 (c) -1

7. If q=\sqrt{5}+2 find(ii) q-\frac{1}{q}
7. If  q=\sqrt{5}+2  find(ii)  q-\frac{1}{q}

7. If q=\sqrt{5}+2 find(ii) q-\frac{1}{q}

6. Perform the indicated operation and simplify.(ii) \frac{4 x-12}{x^{2}-9} \div \frac{18-2 x^{2}}{x^{2}+6 x+9}
6. Perform the indicated operation and simplify.(ii)  \frac{4 x-12}{x^{2}-9} \div \frac{18-2 x^{2}}{x^{2}+6 x+9}

6. Perform the indicated operation and simplify.(ii) \frac{4 x-12}{x^{2}-9} \div \frac{18-2 x^{2}}{x^{2}+6 x+9}

4. Simplify(v) (\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})(x+y)\left(x^{2}+y^{2}\right)
4. Simplify(v)  (\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})(x+y)\left(x^{2}+y^{2}\right)

4. Simplify(v) (\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})(x+y)\left(x^{2}+y^{2}\right)

6. If p=2+\sqrt{3} find(iv) p^{2}-\frac{1}{p^{2}}
6. If  p=2+\sqrt{3}  find(iv)  p^{2}-\frac{1}{p^{2}}

6. If p=2+\sqrt{3} find(iv) p^{2}-\frac{1}{p^{2}}

Example 1Rationalize the denominator \frac{58}{7-2 \sqrt{5}}
Example 1Rationalize the denominator  \frac{58}{7-2 \sqrt{5}}

Example 1Rationalize the denominator \frac{58}{7-2 \sqrt{5}}

2. Find the conjugate of x+\sqrt{y} .(iii) 2+\sqrt{3}
2. Find the conjugate of  x+\sqrt{y} .(iii)  2+\sqrt{3}

2. Find the conjugate of x+\sqrt{y} .(iii) 2+\sqrt{3}

8. Simplify(i) \frac{\sqrt{a^{2}+2}+\sqrt{a^{2}-2}}{\sqrt{a^{2}+2}-\sqrt{a^{2}-2}}
8. Simplify(i)  \frac{\sqrt{a^{2}+2}+\sqrt{a^{2}-2}}{\sqrt{a^{2}+2}-\sqrt{a^{2}-2}}

8. Simplify(i) \frac{\sqrt{a^{2}+2}+\sqrt{a^{2}-2}}{\sqrt{a^{2}+2}-\sqrt{a^{2}-2}}

1. Express each of the following surd in the simplest form.(iv) \sqrt[5]{96 x^{6} y^{7} z^{8}}
1. Express each of the following surd in the simplest form.(iv)  \sqrt[5]{96 x^{6} y^{7} z^{8}}

1. Express each of the following surd in the simplest form.(iv) \sqrt[5]{96 x^{6} y^{7} z^{8}}

1. Express each of the following surd in the simplest form.(i) \sqrt{180}
1. Express each of the following surd in the simplest form.(i)  \sqrt{180}

1. Express each of the following surd in the simplest form.(i) \sqrt{180}

2. Find the conjugate of x+\sqrt{y} .(vii) 7-\sqrt{6}
2. Find the conjugate of  x+\sqrt{y} .(vii)  7-\sqrt{6}

2. Find the conjugate of x+\sqrt{y} .(vii) 7-\sqrt{6}

3. Simplify by combining similar terms.(ii) 4 \sqrt{12}+5 \sqrt{27}-3 \sqrt{75}+\sqrt{300}
3. Simplify by combining similar terms.(ii)  4 \sqrt{12}+5 \sqrt{27}-3 \sqrt{75}+\sqrt{300}

3. Simplify by combining similar terms.(ii) 4 \sqrt{12}+5 \sqrt{27}-3 \sqrt{75}+\sqrt{300}

Example 1If 2 x-3 y=10 and x y=2 then find the value of 8 x^{3}-27 y^{3} .
Example 1If  2 x-3 y=10  and  x y=2  then find the value of  8 x^{3}-27 y^{3} .
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Example 1If 2 x-3 y=10 and x y=2 then find the value of 8 x^{3}-27 y^{3} .

3. Reduce the following rational expressions to the lowest form.(ii) \frac{8 a(x+1)}{2\left(x^{2}-1\right)}
3. Reduce the following rational expressions to the lowest form.(ii)  \frac{8 a(x+1)}{2\left(x^{2}-1\right)}
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3. Reduce the following rational expressions to the lowest form.(ii) \frac{8 a(x+1)}{2\left(x^{2}-1\right)}

4. Simplify(iii) \frac{2}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}+\sqrt{2}}
4. Simplify(iii)  \frac{2}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}+\sqrt{2}}
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4. Simplify(iii) \frac{2}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}+\sqrt{2}}

5. Perform the indicated operation and simplify.(vi) \frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^{2}+1}-\frac{4}{x^{4}-1}
5. Perform the indicated operation and simplify.(vi)  \frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^{2}+1}-\frac{4}{x^{4}-1}
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5. Perform the indicated operation and simplify.(vi) \frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^{2}+1}-\frac{4}{x^{4}-1}

Example 1Factorize 64 x^{3}+343 y^{3}
Example 1Factorize  64 x^{3}+343 y^{3}
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Example 1Factorize 64 x^{3}+343 y^{3}

Example 2Rationalize the denominator \frac{2}{\sqrt{5}+\sqrt{2}}
Example 2Rationalize the denominator  \frac{2}{\sqrt{5}+\sqrt{2}}
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Example 2Rationalize the denominator \frac{2}{\sqrt{5}+\sqrt{2}}

9. If 5 x-6 y=13 and x y=6 then find the value of 125 x^{3}-216 y^{3} .
9. If  5 x-6 y=13  and  x y=6  then find the value of  125 x^{3}-216 y^{3} .
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9. If 5 x-6 y=13 and x y=6 then find the value of 125 x^{3}-216 y^{3} .

3. Reduce the following rational expresions to the lowest form.(i) \frac{120 x^{2} y^{3} z^{5}}{30 x^{3} y z^{2}}
3. Reduce the following rational expresions to the lowest form.(i)  \frac{120 x^{2} y^{3} z^{5}}{30 x^{3} y z^{2}}
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3. Reduce the following rational expresions to the lowest form.(i) \frac{120 x^{2} y^{3} z^{5}}{30 x^{3} y z^{2}}

(vi) \frac{1}{a-b}-\frac{1}{a+b} is equal to(a) \frac{2 a}{a^{2}-b^{2}} (b) \frac{2 b}{a^{2}-b^{2}} (c) \frac{-2 a}{a^{2}-b^{2}} (d) \frac{-2 b}{a^{2}-b^{2}}
(vi)  \frac{1}{a-b}-\frac{1}{a+b}  is equal to(a)  \frac{2 a}{a^{2}-b^{2}} (b)  \frac{2 b}{a^{2}-b^{2}} (c)  \frac{-2 a}{a^{2}-b^{2}} (d)  \frac{-2 b}{a^{2}-b^{2}}
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(vi) \frac{1}{a-b}-\frac{1}{a+b} is equal to(a) \frac{2 a}{a^{2}-b^{2}} (b) \frac{2 b}{a^{2}-b^{2}} (c) \frac{-2 a}{a^{2}-b^{2}} (d) \frac{-2 b}{a^{2}-b^{2}}

(vii) \frac{a^{2}-b^{2}}{a+b} is equal to(a) (a-b)^{2} (b) (a+b)^{2} (c) a+b (d) a-b
(vii)  \frac{a^{2}-b^{2}}{a+b}  is equal to(a)  (a-b)^{2} (b)  (a+b)^{2} (c)  a+b (d)  a-b
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(vii) \frac{a^{2}-b^{2}}{a+b} is equal to(a) (a-b)^{2} (b) (a+b)^{2} (c) a+b (d) a-b

3 . (ii) If x=4-\sqrt{17} find \frac{1}{x}
 3 . (ii) If  x=4-\sqrt{17}  find  \frac{1}{x}
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3 . (ii) If x=4-\sqrt{17} find \frac{1}{x}

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