Subtract. Simplify, if possible.
-$$\frac { - 6 } { y - 8 } - \frac { 4 } { 8 - y }$$
A) $\frac { - 24 } { y - 8 }$

B) $\frac { - 2 } { y - 8 }$

C) $\frac { - 10 } { y - 8 }$

D) $\frac { 10 } { y - 8 }$

Question

Subtract. Simplify, if possible.
-$$\frac { - 6 } { y - 8 } - \frac { 4 } { 8 - y }$$
A) $\frac { - 24 } { y - 8 }$

B) $\frac { - 2 } { y - 8 }$

C) $\frac { - 10 } { y - 8 }$

D) $\frac { 10 } { y - 8 }$

Quizplus · Accepted Answer

To subtract fractions, we need a common denominator. In this case, the common denominator is $(y-8)(-1)=8-y$. Therefore, we can rewrite the expression as:

$$\frac{-6(8-y)}{(y-8)(8-y)}-\frac{4(y-8)}{(8-y)(y-8)}$$

Simplifying the numerators, we get:

$$\frac{-48+6y-4y+32}{(y-8)(8-y)}$$

Combining like terms, we get:

$$\frac{-16+2y}{(y-8)(8-y)}$$

Finally, we can simplify by factoring out a $-2$ in the numerator and cancelling the negative signs in the denominator:

$$\frac{-2(y-8)}{(y-8)(y-8)}=\boxed{	extbf{(B)}\ \frac{-2}{y-8}}$$

Subtract Simplify, If Possible −6y−8−48−y\frac { - 6 } { y - 8 } - \frac { 4 } { 8 - y }y−8−6​−8−y4​

Subtract Simplify, If Possible $\frac { - 6 } { y - 8 } - \frac { 4 } { 8 - y }$