What is (4x^2+4x)/(2x^2-2) ?

The solution to (4x^2+4x)/(2x^2-2) is (2x)/(x-1)

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simplify (4x^2+4x)/(2x^2-2)

simplify

\frac{4 x ^{2} + 4 x}{2 x ^{2} - 2}

\frac{2 x}{x - 1}

Solution steps

\frac{4 x ^{2} + 4 x}{2 x ^{2} - 2}

Factor

4 x^{2} + 4 x : 4 x (x + 1)

= \frac{4 x ( x + 1 )}{2 x ^{2} - 2}

Factor

2 x^{2} - 2 : 2 (x + 1) (x - 1)

= \frac{4 x ( x + 1 )}{2 ( x + 1 ) ( x - 1 )}

Cancel the common factor:

x + 1

= \frac{4 x}{2 ( x - 1 )}

Factor the number:

4 = 2 \cdot 2

= \frac{2 \cdot 2 x}{2 ( x - 1 )}

Cancel the common factor:

2

= \frac{2 x}{x - 1}

\frac{5}{4} \times 4

- 5

1 \frac{11}{25}

x \times x \times x \times x

42 \times 2