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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x - 2, x + 3 : (x - 2) (x + 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 x (x + 3) - (x + 5) (x - 2) : x^{2} + 3 x + 10

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

x (x + 3)

(x - 2) (x + 5)

lo g_{x} (x)

x^{2} \times x

(x + 4)^{2}

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