Question

PLEASE i need help so badly asap

Answer 1

Answer:

13

Step-by-step 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 $c^2-7c-18$

$\frac{5}{c-9}\times(c^2-7c-18)=\frac{5}{c-9}\times(c-9)(c+2)=5(c+2)=5(c)+5(2)=5c+10$

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

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

$\frac{5c-2}{c^2-7c-18}\times(c^2-7c-18)=5c-2$

$\frac{3}{c+2}\times(c^2-7c-18)=\frac{3}{c+2}\times(c-9)(c+2)=3(c-9)=3c-27$

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

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

Therefore,

c = 13