Question

To eliminate the denominators in the equation $\frac{3}{x}+\frac{5}{x+2}=2$, we multiply each side by the lowest common denominator ___ to get the equivalent equation ___

Short answer

To eliminate the denominators in the equation $\frac{3}{x}+\frac{5}{x+2}=2$, we multiply each side by the lowest common denominator $x\left(x+2\right)$to get the equivalent equation$3\left(x+2\right)+5x=2x\left(x+2\right)$

Step-by-step solution

Step 1. Apply the concept of quadratic equations.

A quadratic equation is an equation of the form$a{x}^2+bx+c=0$ where a, b, and c are real numbers with$a\ne 0$

Step 2. Analyze the given expression.

Given

$\frac{3}{x}+\frac{5}{x+2}=2$

Step 3. Solve.

The denominators are$x,x+2$

The lowest common denominator is$x\left(x+2\right)$

We multiply each side by lowest common denominator $x\left(x+2\right)$to get the equivalent equation

localid="1643287657659" $\begin{array}{l}\left(\frac{3}{x}+\frac{5}{x+2}\right)x\left(x+2\right)=2x\left(x+2\right)\\ \Rightarrow \left(\frac{3\left(x+2\right)+5x}{x\left(x+2\right)}\right)x\left(x+2\right)=2x\left(x+2\right)\\ \Rightarrow 3\left(x+2\right)+5x=2x\left(x+2\right)\end{array}$