Question

Express the given fraction in terms of x, $\frac{(a+b{)}^2}{2ab}$ if x= $\frac{a}{b}$

• A. $\frac{(x^2+1)}{2x}+1$
• B. $\frac{(x^2+1)}{3x}+1$
• C. $x^2+1$
• D. $\frac{x^2}{2}+1$

Answer 1

The correct option is A

$\frac{(x^2+1)}{2x}+1$

Give algebraic fraction is: $\frac{(a+b{)}^2}{2ab}$

$(a+b{)}^2=a^2+2ab+b^2$

Now, $\frac{(a+b{)}^2}{2ab}$ $\Rightarrow$ $\frac{a^2}{2ab}+\frac{b^2}{2ab}+1$

$\Rightarrow$ $\frac{a}{2b}+\frac{b}{2a}+1$

Taking, $\frac{1}{2}$ common

$\Rightarrow$ $\frac{1}{2}[\frac{a}{b}+\frac{b}{a}]+1$

As x = $\frac{a}{b}$, the expression turns to $\frac{1}{2}[x+\frac{1}{x}]+1$

$\Rightarrow$ $\frac{(x^2+1)}{2x}+1$