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

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

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factor x/(x+2)-3/(2x+3)

factor

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

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

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

Factor

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

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

\frac{4}{n + 7} - \frac{7}{n - 2}

∣ x + 2 ∣ + ∣ x ∣ \leq 2

∣ 4 m + 2 ∣ \geq 6

x^{4} + 9 x^{3} < x + 9

x^{2} - 19 = 2 x

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