Question

Can you help me with part E of the question?

Answer 1

Question:

Solution:

We want to solve the following equation:

$\frac{4x+12}{x^2-5x}=-\frac{10}{3}$

that is:

$\frac{4x+12}{x^2-5x}=\frac{-10}{3}$

by cross-multiplication, this is equivalent to:

$3(4x+12)=-10(x^2-5x\text{)}$

applying the distributive property, we obtain:

$12x+36=-10x^2+50x$

this is equivalent to:

$10x^2+12x-50x+36=0$

that is:

$10x^2-38x+36=0$

now, applying the quadratic formula, we obtain two solutions:

$x=\text{ 2}$

and

$x=\frac{9}{5}$

so that, we can conclude that the correct answer is:

$x=\text{ 2}$

or

$x=\frac{9}{5}$