Find the least common denominator (LCD). $$\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }$$
A) $y ^ { 3 } ( y - 8 ) ^ { 3 }$
B) $y ^ { 2 } ( y - 8 ) ^ { 2 }$
C) $y ^ { 2 }$
D) $y ^ { 2 } - 16 y + 64$

Question

Quizplus · Accepted Answer

The least common denominator (LCD) must account for all different factors in the denominators of the given fractions. The denominators are $y^2$, $y^2 - 8y$, and $y^2 - 16y + 64$. Factoring each:1. $y^2$ is already factored.2. $y^2 - 8y = y^2 - 2\cdot4y = y(y - 8)$.3. $y^2 - 16y + 64 = (y - 8)^2$, since $64 = 8^2$.The LCD needs to include $y^2$ to account for the first fraction, and $y(y - 8)$ to account for the second fraction. For the third fraction, $(y - 8)^2$ is needed. Combining these, the LCD is $y^2(y - 8)^2$, which is option B.

Find the Least Common Denominator (LCD) 8y+2y2,2y2−8y,−2y3y2−16y+64\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }y28y+2​,y2−8y2​,y2−16y+64−2y3​

Find the Least Common Denominator (LCD) $\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }$