Question

What is the solution to the rational equation x over x squared minus 9 plus 1 over x plus 3 equals 1 over 4x minus 12 ?

Answer 1

\[\huge\rm
\frac{ x }{ x^2-9}+\frac{ 1 }{ x+3}=\frac{ 1 }{ 4x-12 }\] like this ?

Answer 2

yes

Answer 3

alright first solve left side
apply difference of square method to factor x^2-9 \[\rm a^2-b^2=(a+b)(a-b)\]

Answer 4

take square of both terms
write ur answer as (sqrt of 1st term + sqrt of 2nd term) (sqrt of 1st term - sqrt of 2nd term)
here is an example \[\rm x^2-16=(x+4)(x-4)\]

Answer 5

x = -9 over 7
x = 15
x = 15 over 7
x = 9

Answer 6

these are the answers i have

Answer 7

ok.
so what are the factors of x^2-9 ?

Answer 8

(x-9)(x+9)

Answer 9

hmm not
what is the square root of 9 ?

Answer 10

3