Question

Plz solve this question​

Answer 1

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

• Simplify ⇨ 1/x(x+a) + 1/x(x-a)

$\large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}$

$\sf\frac { 1 } { x ( x + a ) } + \frac { 1 } { x ( x - a ) }$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x\left(x+a\right)$ and $x\left(x-a\right)$ is $x\left(x+a\right)\left(x-a\right)$. Multiply $\frac{1}{x\left(x+a\right)} times \frac{x-a}{x-a}$. Multiply $\frac{1}{x\left(x-a\right)} times \frac{x+a}{x+a}$.

$\sf\frac{x-a}{x\left(x+a\right)\left(x-a\right)}+\frac{x+a}{x\left(x+a\right)\left(x-a\right)}$

Because $\frac{x-a}{x\left(x+a\right)\left(x-a\right)}$ and $\frac{x+a}{x\left(x+a\right)\left(x-a\right)}$ have the same denominator, add them by adding their numerators.

$\sf\frac{x-a+x+a}{x\left(x+a\right)\left(x-a\right)}$

Combine like terms in x-a+x+a.

$\sf\frac{2x}{x\left(x+a\right)\left(x-a\right)}$

Cancel out x in both the numerator and denominator.

$\sf\frac{2}{\left(x+a\right)\left(x-a\right)}$

Expand $\left(x+a\right)\left(x-a\right)$.

$\boxed{\boxed{ \bf\frac{2}{x^{2}-a^{2}}}}$