Question

Can you help me with part E of the question?

Answer 1

Question:

Solution:

We want to solve the following equation:

`(4x+12)/(x^2-5x)=-(10)/(3)`

that is:

`(4x+12)/(x^2-5x)=(-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=(9)/(5)`

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

`x=\text{ 2}`

or

`x=(9)/(5)`