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

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

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

simplify

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

\frac{1}{( x + 3 ) ( x + 2 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel the common factor:

x

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

\frac{( 6 x ^{3} \cdot y - 12 x ^{2} \cdot y ^{2} + 7 x y )}{( - 3 x y )}

f (- 5) \cdot g (2)

15 + (- 12) y + 24

(2 a^{5})^{- 3}

(x^{2} + 1 + y) (x^{2} + 1 - y)

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