Test Index

UPSC CDS 2 2020 Math Paper

© examsnet.com

Question : 77 of 100

Marks: +1, -0

What is the value of

\frac{a^{2}+a c}{a^{2} c-c^{3}}-\frac{a^{2}-c^{2}}{a^{2}c+2 a c^{2}+c^{3}}-\frac{2 c}{a^{2}-c^{2}}

+\frac{3}{a+c} \\ ?

0
1
$\frac{a c}{a^{2}-c^{2}}$
$\frac{6}{a+c}$

Solution:

we have

\frac{a^{2}+a c}{a^{2} c-c^{3}}-\frac{a^{2}-c^{2}}{a^{2}+2 a c^{2}+c^{3}}-\frac{2 c}{a^{2}-c^{2}}

+\frac{3}{a+c}

\Rightarrow \frac{a(a+c)}{c(a-c)(a+c)}-\frac{(a+c)(a-c)}{c(a+c)^{2}}

-\frac{2 c}{(a-c)(a+c)}+\frac{3}{a+c}

\Rightarrow \frac{a}{c(a-c)}-\frac{a-c}{c(a+c)}

-\frac{2 c}{(a-c)(a+c)}+\frac{3}{a+c}

\Rightarrow \frac{a^{2}+a c-a^{2}+2 a c-c^{2}}{c(a^{2}-c^{2})}

-\frac{2 c-3 a+3 c}{a^{2}-c^{2}}

\Rightarrow \frac{c(3 a-c)}{c(a^{2}-c^{2})}+\frac{3 a-5 c}{a^{2}-c^{2}}

\Rightarrow \frac{3 a-c+3 a-5 c}{a^{2}-c^{2}}

\Rightarrow \frac{6(a-c)}{a^{2}-c^{2}}

⇒

\frac{6}{a+c}

© examsnet.com

Go to Question:

Prev Question

Next Question