Question

$\frac{4x^2}{2x-1}$ can be written as $\frac{1}{2x-1}+A$. Find $A$ in terms of $x$.

• A. $2x+1$
• B. $2x-1$
• C. $4x^2$
• D. $4x^2-1$

Answer 1

The correct option is A $2x+1$

We have $\frac{4x^2}{2x-1}=\frac{1}{2x-1}+A$

We can write $\frac{4x^2}{2x-1}=\frac{(4x^2-1)+1}{2x-1}$

$\Rightarrow \frac{(2x+1)(2x-1)+1}{2x-1}=(2x+1)+\frac{1}{2x-1}$
On comparing, we get

$A=2x+1$