What is (3x-4)/(x^2-9)+(2x-1)/(x+3) ?

The solution to (3x-4)/(x^2-9)+(2x-1)/(x+3) is (2x^2-4x-1)/((x+3)(x-3))

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simplify (3x-4)/(x^2-9)+(2x-1)/(x+3)

simplify

\frac{3 x - 4}{x ^{2} - 9} + \frac{2 x - 1}{x + 3}

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

Solution steps

\frac{3 x - 4}{x ^{2} - 9} + \frac{2 x - 1}{x + 3}

Least Common Multiplier of

x^{2} - 9, x + 3 : (x + 3) (x - 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

(7 x + 6) (7 x - 6)

\frac{12}{45}

lo g_{4} (125)

(u - v)^{2} + (u + v)^{2}

What is (3x-4)/(x^2-9)+(2x-1)/(x+3) ?
The solution to (3x-4)/(x^2-9)+(2x-1)/(x+3) is (2x^2-4x-1)/((x+3)(x-3))