Question

Add:
4/x^2-10x+24 + x+1/x-4

Answer 1

\[\frac{ 4 }{ x ^{2}-10x+24 } + \frac{ x+1 }{ x-4 }\]

Answer 2

lets factor out the \[x^2-10x+24\]

Answer 3

So x(x-12)(x+2) ?

Answer 4

Oh wait that would make -24 @_@.

Answer 5

:)

Answer 6

Or is that right?

Answer 7

nope. thats wrong
two numbers that multiply to +24
and add up to -10

Answer 8

-6 & -4

Answer 9

bingo
so, the factors are:
\[(x-6)(x-4)\]

Answer 10

x(x-6)(x-4) right?

Answer 11

now, lets write the give expression again
\[
{4\over(x-6)(x-4)}+{x+1\over x-4}
\]

Answer 12

there are only two terms
no neeed for the extra "x"

Answer 13

now, just like the regular fractions, we make the denominator common

Answer 14

\[
{4\over(x-6)(x-4)}+{x+1\over x-4}\times{x-6\over x-6}
\]

Answer 15

\[
=\frac{4+(x+1)(x-6)}{(x-6)(x-4)}\\
=\frac{4+x^2-6x+x-6}{(x-6)(x-4)}\qquad\text{I expanded the product}\\
=\frac{x^2-5x-2}{(x-6)(x-4)}
\]
The numerator cannot be simplified easily. so, we can leave our answer here

Answer 16

Thanks so much! :)

Answer 17

yw