What is expand (1/5)/(y-3)-(1/5)/(y+2) ?

The solution to expand (1/5)/(y-3)-(1/5)/(y+2) is 1/(y^2-y-6)

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expand (1/5)/(y-3)-(1/5)/(y+2)

expand

\frac{\frac{1}{5}}{y - 3} - \frac{\frac{1}{5}}{y + 2}

\frac{1}{y ^{2} - y - 6}

Solution steps

\frac{\frac{1}{5}}{y - 3} - \frac{\frac{1}{5}}{y + 2}

\frac{\frac{1}{5}}{y - 3} = \frac{1}{5 y - 15}

\frac{\frac{1}{5}}{y + 2} = \frac{1}{5 y + 10}

= \frac{1}{5 y - 15} - \frac{1}{5 y + 10}

Factor

5 y - 15 : 5 (y - 3)

= \frac{1}{5 ( y - 3 )} - \frac{1}{5 y + 10}

Factor

5 y + 10 : 5 (y + 2)

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

Least Common Multiplier of

5 (y - 3), 5 (y + 2) : 5 (y - 3) (y + 2)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

5 (y - 3) (y + 2) : 5 y^{2} - 5 y - 30

= \frac{y + 2 - ( y - 3 )}{5 y ^{2} - 5 y - 30}

Expand

y + 2 - (y - 3) : 5

= \frac{5}{5 y ^{2} - 5 y - 30}

Factor

5 y^{2} - 5 y - 30 : 5 (y^{2} - y - 6)

= \frac{5}{5 ( y ^{2} - y - 6 )}

Divide the numbers:

\frac{5}{5} = 1

= \frac{1}{( y ^{2} - y - 6 )}

Remove parentheses:

(a) = a

= \frac{1}{y ^{2} - y - 6}

\frac{d}{d x} ((z (x, y)) (6 x^{5} + 4 y^{3} + 4 y))

(sin (θ) + cos (θ) sin (θ)) sin (θ)

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

5 x + 4 (- 4 x + 1)

What is expand (1/5)/(y-3)-(1/5)/(y+2) ?
The solution to expand (1/5)/(y-3)-(1/5)/(y+2) is 1/(y^2-y-6)