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

The solution to (2x+3)/(x-4)-(x-5)/(x+2) is (x^2+16x-14)/((x-4)(x+2))

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

simplify

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

\frac{x ^{2} + 16 x - 14}{( x - 4 ) ( x + 2 )}

Solution steps

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

Least Common Multiplier of

x - 4, x + 2 : (x - 4) (x + 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(2 x + 3) (x + 2) - (x - 5) (x - 4) : x^{2} + 16 x - 14

= \frac{x ^{2} + 16 x - 14}{( x - 4 ) ( x + 2 )}

\frac{x + 1}{x ^{2} + 6 x + 9} + \frac{x - 4}{x ^{2} - 9}

\frac{x ^{2} - 14 x + 45}{x ^{2} - 18 x + 81}

lo g_{10} (\frac{1}{10})

(3 x + 4 b) (3 x - 4 b)

1 0^{- 2.3}

What is (2x+3)/(x-4)-(x-5)/(x+2) ?
The solution to (2x+3)/(x-4)-(x-5)/(x+2) is (x^2+16x-14)/((x-4)(x+2))