Question

Linear Equations The given equation is either linear or equivalent to a linear equation. Solve the equation.

$\frac{4}{x-1}+\frac{2}{x+1}=\frac{35}{x^2-1}$

Short answer

The solution of the given equation is $x=\frac{11}{2}$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$\frac{4}{x-1}+\frac{2}{x+1}=\frac{35}{x^2-1}$

Step 3. Solve the given equation.

The given equation can be written as:

$\frac{4\left(x+1\right)+2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{35}{\left(x-1\right)\left(x+1\right)}$

Multiply both sides by$\left(x-1\right)(x+1)$ to simplify the above equation.

role="math" localid="1643313123544" $\begin{array}{c}\left(x-1\right)\left(x+1\right)\times \frac{4\left(x\right)+4\left(1\right)+2\left(x\right)+2\left(-1\right)}{\left(x-1\right)\left(x+1\right)}=\left(x-1\right)\left(x+1\right)\times \frac{35}{\left(x-1\right)\left(x+1\right)}\\ 4x+4+2x-2=35\\ 6x+2=35\end{array}$

Subtract$2$ from both sides.

$\begin{array}{c}6x+2-2=35-2\\ 6x=33\end{array}$

Divide both sides by $6$.

role="math" localid="1643313201091" $\begin{array}{c}\frac{6x}{6}=\frac{33}{6}\\ x=\frac{11}{2}\end{array}$

Thus, the solution of the given equation is $x=\frac{11}{2}$.