# How do you simplify an algebra expression with fraction bars?

May 14, 2015

It depends on the expression:

$\frac{x}{4} + 2 = \frac{x}{4} + \frac{8}{4} = \frac{x + 8}{4}$

$\frac{2 x}{x + 1} + \frac{5}{x + 1} = \frac{2 x + 5}{x + 1}$

$\frac{3 x - 2}{5} + \frac{x - 7}{x} = \frac{\left(3 x - 2\right) x}{5 x} + \frac{\left(x - 7\right) 5}{5 x} = \frac{\left(3 {x}^{2} - 2 x\right) + \left(5 x - 35\right)}{5 x} = \frac{3 {x}^{2} + 3 x - 35}{5 x}$

$\frac{3 x}{\sqrt{2}} = \frac{3 x}{\sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}} = \frac{3 x \sqrt{2}}{2}$

$\frac{{x}^{2} - 1}{{x}^{2} - 4 x - 5} = \frac{\left(x + 1\right) \left(x - 1\right)}{\left(x + 1\right) \left(x - 5\right)} = \frac{x + 1}{x - 5}$

Post a particular problem.