Question

What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared minus 14x minus 15 ? @SolomonZelman @midhun.madhu1987 @FriedRice14

Answer 1

@anonymous_user

Answer 2

@kirbykirby

Answer 3

\[ \frac{3}{4x+3}+\frac{21}{8x^2-14x-15}\]? ?

Answer 4

Right

Answer 5

WHat you could do is factor the denominator of the 2nd fraction:
\(8x^2 -14x-15 = 8x^2+6x-20x-15 = 2x(4x+3)-5(4x+3)=(4x+3)(2x-5)\)

Answer 6

The last thing is just (2x-5), just the parenthesis just got cutt off

Answer 7

that's it?

Answer 8

No that's one step

Answer 9

You can then combine the 2 fractions into one by multiplying the top and bottom of the first fraction by (2x-5):

\[ \frac{3}{4x+3}+\frac{21}{(4x+3)(2x-5)}\\ ~ \\=\frac{3}{(4x+3)}\frac{(2x-5)}{(2x-5)}+\frac{21}{(4x+3)(2x-5)}\\~\\=\frac{3(2x-5)+21}{(4x+3)(2x-5)} \\ ~ \\ =\frac{6x-15+21}{(4x+3)(2x-5)} \\ ~ \\ \frac{6(x+1)}{(4x+3)(2x-5)}\]

Answer 10

now i'm not sure if your teacher wants you to keep the top and bottom as factors or expanded out..

Answer 11

This is good thanks

Answer 12

yw!