What is (5x-3)/(x+1)+6/(x-2) ?

The solution to (5x-3)/(x+1)+6/(x-2) is (5x^2-7x+12)/((x+1)(x-2))

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simplify (5x-3)/(x+1)+6/(x-2)

simplify

\frac{5 x - 3}{x + 1} + \frac{6}{x - 2}

\frac{5 x ^{2} - 7 x + 12}{( x + 1 ) ( x - 2 )}

Solution steps

\frac{5 x - 3}{x + 1} + \frac{6}{x - 2}

Least Common Multiplier of

x + 1, x - 2 : (x + 1) (x - 2)

Adjust Fractions based on the LCM

= \frac{( 5 x - 3 ) ( x - 2 )}{( x + 1 ) ( x - 2 )} + \frac{6 ( x + 1 )}{( x + 1 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{( 5 x - 3 ) ( x - 2 ) + 6 ( x + 1 )}{( x + 1 ) ( x - 2 )}

Simplify

(5 x - 3) (x - 2) + 6 (x + 1) : 5 x^{2} - 7 x + 12

= \frac{5 x ^{2} - 7 x + 12}{( x + 1 ) ( x - 2 )}

6 + \frac{16 - 4}{2 ^{2} + 2} - 2

\frac{8}{2 - 2}

52 + 2 - 32

x^{2} (x + 4) + 3 x (x + 4) - 70 (x + 4)

e^{0} 0 + 3 e^{0}

What is (5x-3)/(x+1)+6/(x-2) ?
The solution to (5x-3)/(x+1)+6/(x-2) is (5x^2-7x+12)/((x+1)(x-2))