What is (3x+2)/(x-7)-(2x)/(x^2-5x-14) ?

The solution to (3x+2)/(x-7)-(2x)/(x^2-5x-14) is (3x^2+6x+4)/((x-7)(x+2))

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simplify (3x+2)/(x-7)-(2x)/(x^2-5x-14)

simplify

\frac{3 x + 2}{x - 7} - \frac{2 x}{x ^{2} - 5 x - 14}

\frac{3 x ^{2} + 6 x + 4}{( x - 7 ) ( x + 2 )}

Solution steps

\frac{3 x + 2}{x - 7} - \frac{2 x}{x ^{2} - 5 x - 14}

Least Common Multiplier of

x - 7, x^{2} - 5 x - 14 : (x - 7) (x + 2)

Adjust Fractions based on the LCM

= \frac{( 3 x + 2 ) ( x + 2 )}{( x - 7 ) ( x + 2 )} - \frac{2 x}{( x - 7 ) ( x + 2 )}

Apply the fraction rule:

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

= \frac{( 3 x + 2 ) ( x + 2 ) - 2 x}{( x - 7 ) ( x + 2 )}

Simplify

(3 x + 2) (x + 2) - 2 x : 3 x^{2} + 6 x + 4

= \frac{3 x ^{2} + 6 x + 4}{( x - 7 ) ( x + 2 )}

lo g_{5} (5^{\frac{1}{4}})

3 x y^{2} \cdot \frac{x - y}{3 x y}

(2 x + 3 y) (3 x + 2 y)

36 x^{10}

What is (3x+2)/(x-7)-(2x)/(x^2-5x-14) ?
The solution to (3x+2)/(x-7)-(2x)/(x^2-5x-14) is (3x^2+6x+4)/((x-7)(x+2))