Question

PLEASE i need help so badly asap

Answer 1

13

Explanation:

We can multiply both the whole equation by
`c^2-7c-18`. This is the LCM of all of the denominators. Notice that when
`c^2-7c-18` is factored, we obtain
`(c - 9)(c+2)`.

Step 1: Multiply Left Side by
`c^2-7c-18`

`(5)/(c-9)*(c^2-7c-18)=(5)/(c-9)*(c-9)(c+2)=5(c+2)=5(c)+5(2)=5c+10`

Step 2: Multiply Right Side by
`c^2-7c-18`

An easier approach is to multiply each individual fraction like so:

`(5c-2)/(c^2-7c-18)*(c^2-7c-18)=5c-2`

`(3)/(c+2)*(c^2-7c-18)=(3)/(c+2)*(c-9)(c+2)=3(c-9)=3c-27`

Then, we add them:

`5c-2+(3c-27)=5c-2+3c-27=8c-29`

Therefore the whole equation is now:

`5c+10=8c-29`

Step 3: Solve for "c"

Subtract 5c from both sides:

`10=3c-29`

Add 29 to both sides:

`39=3c`

Divide both sides by 3

`c=13`

Step 4: Plug 13 in for "c" to check our work

`(5)/(13-9)=(5(13)-2)/(169-91-14)+(3)/(13+2)\\\\(5)/(4)=(63)/(60)+(3)/(15)\\\\(5)/(4)=(21)/(20)+(1)/(5)\\\\(5)/(4)=(21)/(20)+(1)/(5)\\\\(5)/(4)=(21)/(20)+(4)/(20)\\\\(5)/(4)=(25)/(20)\\\\(5)/(4)=(5)/(4)\Rightarrow Correct!`

Therefore,

c = 13