Simplify the following expression by canceling, if possible:
Answer
x
Example 2
Simplify the following expression by canceling, if possible:
Answer
First off, factor the numerator by grouping to get 10x2(4x + 7) + 9(4x + 7) = (10x2 + 9)(4x + 7) up top. Then pull out a common factor of (4x + 7) from the bottom and cancel like there's no tomorrow to find .
Example 3
Simplify the following expression by canceling, if possible:
Answer
(2x + 3)(4x – 1) = 8x2 + 10x – 3
Example 4
Simplify the following expression by canceling, if possible:
Answer
Factors as . Can't be simplified.
Example 5
Simplify the following expression by canceling, if possible:
Answer
We can factor the numerator and denominator by grouping. First rearrange the numerator:
3x2y + xy2 – 12x – 4y =
xy(3x + y) – 4(3x + y) =
(xy – 4)(3x + y)
Then we group the denominator:
3xy + 6x + y2 + 2y =
3x(y + 2) + y(y + 2) =
(3x + y)(y + 2)
Finish up by canceling out that 3x + y term from the top and bottom to get . Whew, time to hydrate.
.
. Can't be simplified.
. Whew, time to hydrate.