Question

If you are solving the equation 1/(x-4)+1=14/(x+2) by factoring, which of the following equations would you use the zero product property on?

(x - 5)(x + 4) = 0
(x - 5)(x - 10) = 0
(x + 5)(x + 10) = 0

Answer 1

So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0

Option B is correct.

Explanation:

Answer 2

The equation that would be used for the zero product property on will be (x-5)(x-10)=0

Option B is correct.

Explanation:

We need to solve the equation
`(1)/((x-4))+1=(14)/(x+2)`

Solving the equation:

`(1)/((x-4))+1=(14)/(x+2)\\(1+(x-4))/(x-4)= (14)/(x+2)\\(1+x-4)/(x-4)= (14)/(x+2)\\(x-3)/(x-4)= (14)/(x+2)\\Cross\: Multiply\\(x-3)(x+2)=14(x-4)\\x(x+2)-3(x+2)=14x-56\\x^2+2x-3x-6=14x-56\\x^2-x-6-14x+56=0\\x^2-x-14x-6+50=0\\x^2-15x+50=0`

Now, we would factorise to find value of x

`x^2-15x+50=0\\x^2-5x-10x+50=0\\x(x-5)-10(x-5)=0\\(x-5)(x-10)=0`

So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0

Option B is correct.