# algebra - 05

## 01. The simplified value of following is: (315a5b6c3×59ab5c4)$\left(\frac{3}{15}{a}^{5}{b}^{6}{c}^{3}×\frac{5}{9}a{b}^{5}{c}^{4}\right)$\left( {\frac{3}{{15}}{a^5}{b^6}{c^3} \times \frac{5}{9}a{b^5}{c^4}} \right)     ÷ 1017a2bc3$\frac{10}{17}{a}^{2}b{c}^{3}$\frac{{10}}{{17}}{a^2}b{c^3}

• 1
$\frac{3}{10}a{b}^{4}{c}^{3}$
• 2
$\frac{9}{10}{a}^{2}b{c}^{4}$
• 3
$\frac{9}{10}{a}^{2}b{c}^{4}$
• 4
$\frac{1}{10}{a}^{4}{b}^{4}{c}^{10}$

## 05. If xy = a+2a−2,\frac{x}{y}{\text{ = }}\frac{{a + 2}}{{a - 2}}{\text{,}}   then the value of x2−y2x2+y2$\frac{{x}^{2}-{y}^{2}}{{x}^{2}+{y}^{2}}$\frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}   = ?

• 1
$\frac{2a}{{a}^{2}+2}$
• 2
$\frac{4a}{{a}^{2}+4}$
• 3
$\frac{2a}{{a}^{2}+4}$
• 4
$\frac{4a}{{a}^{2}+2}$

## 08. If x+1x−1=ab$\frac{x+1}{x-1}=\frac{a}{b}$\frac{{x + 1}}{{x - 1}} = \frac{a}{b}   and 1−y1+y=ba,$\frac{1-y}{1+y}=\frac{b}{a}\text{,}$\frac{{1 - y}}{{1 + y}} = \frac{b}{a}{\text{,}}   then the value of x−y1+xy$\frac{x-y}{1+xy}$\frac{{x - y}}{{1 + xy}}   is?

• 1
$\frac{{a}^{2}-{b}^{2}}{ab}$
• 2
$\frac{{a}^{2}+{b}^{2}}{2ab}$
• 3
$\frac{{a}^{2}-{b}^{2}}{2ab}$
• 4
$\frac{2ab}{{a}^{2}-{b}^{2}}$

## 10. The sum of 1x+y$\frac{1}{x+y}$\frac{1}{{x + y}}  and 1x−y$\frac{1}{x-y}$\frac{1}{{x - y}}  is?

• 1
$\frac{2y}{{x}^{2}-{y}^{2}}$
• 2
$\frac{2x}{{x}^{2}-{y}^{2}}$
• 3
$\frac{-2y}{{x}^{2}-{y}^{2}}$
• 4
$\frac{2x}{{y}^{2}-{x}^{2}}$
Page 1 Of 2