What is (y^2-2y-15)/4*8/(y+3) ?

The solution to (y^2-2y-15)/4*8/(y+3) is 2y-10

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simplify (y^2-2y-15)/4*8/(y+3)

simplify

\frac{y ^{2} - 2 y - 15}{4} \cdot \frac{8}{y + 3}

2 y - 10

Solution steps

\frac{y ^{2} - 2 y - 15}{4} \cdot \frac{8}{y + 3}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( y ^{2} - 2 y - 15 ) \cdot 8}{4 ( y + 3 )}

Factor the number:

8 = 4 \cdot 2

= \frac{( y ^{2} - 2 y - 15 ) \cdot 4 \cdot 2}{4 ( y + 3 )}

Cancel the common factor:

4

= \frac{( y ^{2} - 2 y - 15 ) \cdot 2}{y + 3}

Factor

y^{2} - 2 y - 15 : (y + 3) (y - 5)

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

Cancel the common factor:

y + 3

= (y - 5) \cdot 2

Expand

(y - 5) \cdot 2 : 2 y - 10

= 2 y - 10

\frac{43}{12}

- 45 + 21

(7 - 3) (7 + 3)

16 + 3

18 + 3