What is (x^2+3x-2)/(x^2-4)+(x^2-2x+4)/(x^2-4) ?

The solution to (x^2+3x-2)/(x^2-4)+(x^2-2x+4)/(x^2-4) is (2x^2+x+2)/(x^2-4)

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simplify (x^2+3x-2)/(x^2-4)+(x^2-2x+4)/(x^2-4)

simplify

\frac{x ^{2} + 3 x - 2}{x ^{2} - 4} + \frac{x ^{2} - 2 x + 4}{x ^{2} - 4}

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

Solution steps

\frac{x ^{2} + 3 x - 2}{x ^{2} - 4} + \frac{x ^{2} - 2 x + 4}{x ^{2} - 4}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{x ^{2} + 3 x - 2 + x ^{2} - 2 x + 4}{x ^{2} - 4}

Simplify

x^{2} + 3 x - 2 + x^{2} - 2 x + 4 : 2 x^{2} + x + 2

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

- 2 x^{2} - 18 x - 36

- 3 x + 4 x

- 3 x + 12

(2 b)^{2}

What is (x^2+3x-2)/(x^2-4)+(x^2-2x+4)/(x^2-4) ?
The solution to (x^2+3x-2)/(x^2-4)+(x^2-2x+4)/(x^2-4) is (2x^2+x+2)/(x^2-4)