Question

What is the solution to the equation m/m+4+4/4-m=m^2/m^2-16

Answer 1

Answer:

B) -2

Step-by-step explanation:

Answer 2

Answer:

The solution is m = -2

Step-by-step explanation:

The given rational equation is

$\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^2}{m^2-16}$

We'll simplify the left hand side first.

The LCD is (m+4)(4-m)

Hence, multiply and divide the first term by 4-m and second by m +4

$\frac{m(4-m)}{(m+4)(4-m)}+\frac{4(m+4)}{(4-m)(m+4}=\frac{m^2}{m^2-16}$

Use the difference of squares rule $a^2-b^2=(a+b)(a-b)$

$\frac{m(4-m)}{4^2-m^2}+\frac{4(m+4)}{4^2-m^2}=\frac{m^2}{m^2-16}$

We can now add the numerator

$\frac{m(4-m)+4(m+4)}{4^2-m^2}=\frac{m^2}{m^2-16}$

On simplifying, we get

$\frac{4m-m^2+4m+16}{16-m^2}=\frac{m^2}{m^2-16}$

Add the like terms

$\frac{8m-m^2+16}{16-m^2}=\frac{m^2}{m^2-16}$

Multiply and divide left hand side by -1

$\frac{m^2-8m-16}{m^2-16}=\frac{m^2}{m^2-16}$

We can cancel the denominator

$-8m-16=0\\8m=-16$

Divide both sides by 8

$m=-2$

The solution is m = -2