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

Answer:

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

Option B is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{(x-4)}+1=\frac{14}{x+2}$

Solving the equation:

$\frac{1}{(x-4)}+1=\frac{14}{x+2}\\\frac{1+(x-4)}{x-4}= \frac{14}{x+2}\\\frac{1+x-4}{x-4}= \frac{14}{x+2}\\\frac{x-3}{x-4}= \frac{14}{x+2}\\Cross\: Multiply\\(x-3)(x+2)=14(x-4)\\x(x+2)-3(x+2)=14x-56\\x^2+2x-3x-6=14x-56\\x^2-x-6-14x+56=0\\x^2-x-14x-6+50=0\\x^2-15x+50=0$

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.

Answer 2

Answer:

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

Option B is correct.

Step-by-step explanation: