Question

Solve for x ac%7Ba%7D%7Bb%2Bc%7D%20" id="TexFormula1" title=" \frac{a}{x} + \frac{b}{c} = \frac{a}{b+c} " alt=" \frac{a}{x} + \frac{b}{c} = \frac{a}{b+c} " align="absmiddle" class="latex-formula">

Answer 1

Easy
make denomenators the same

Step 1
multiply both sidesby (x)(c)(b+c)
(a)(c)(b+c)+(b)(x)(b+c)=(a)(x)(c)

Step 2
distribute
acb+ac²+xb²+bxc=axc

Step 3
minus (acb+ac²) from both sides
xb²+bxc=axc-acb-ac²

Step 4
minus axc from both sides
xb²+bxc-axc=-acb-ac²

Step 5
undistribute x
x(b²+bc-ac)=-acb-ac²

Step 6
divide both sides by (b²+bc-ac)
$x= \frac{-acb-ac^2}{b^2+bc-ac} =\frac{acb+ac^2}{ac-b^2-bc}$