What is (2x)/(x^2-3x-4)+3/(5x^2-20x) ?

The solution to (2x)/(x^2-3x-4)+3/(5x^2-20x) is (10x^2+3x+3)/(5x(x+1)(x-4))

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simplify (2x)/(x^2-3x-4)+3/(5x^2-20x)

simplify

\frac{2 x}{x ^{2} - 3 x - 4} + \frac{3}{5 x ^{2} - 20 x}

\frac{10 x ^{2} + 3 x + 3}{5 x ( x + 1 ) ( x - 4 )}

Solution steps

\frac{2 x}{x ^{2} - 3 x - 4} + \frac{3}{5 x ^{2} - 20 x}

Least Common Multiplier of

x^{2} - 3 x - 4, 5 x^{2} - 20 x : 5 x (x + 1) (x - 4)

Adjust Fractions based on the LCM

= \frac{10 x ^{2}}{5 x ( x + 1 ) ( x - 4 )} + \frac{3 ( x + 1 )}{5 x ( x + 1 ) ( x - 4 )}

Apply the fraction rule:

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

= \frac{10 x ^{2} + 3 ( x + 1 )}{5 x ( x + 1 ) ( x - 4 )}

Simplify

10 x^{2} + 3 (x + 1) : 10 x^{2} + 3 x + 3

= \frac{10 x ^{2} + 3 x + 3}{5 x ( x + 1 ) ( x - 4 )}

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

6 x \cdot 2 x

1 \cdot 5

lo g_{2} (4^{2} \cdot 3^{4})

- 8 \times 4

What is (2x)/(x^2-3x-4)+3/(5x^2-20x) ?
The solution to (2x)/(x^2-3x-4)+3/(5x^2-20x) is (10x^2+3x+3)/(5x(x+1)(x-4))