For what value of the variable is each of the following fractions equal to zero

Question

x(x+1)/x+4

x(x+1)x+4

Answer 1

Only the first one here is a fraction, so perhaps you copied the second one incorrectly. Nonetheless, we can certainly solve the fraction.

 

As fractions are considered "undefined" if the denominator equals zero, the only way for a fraction to equal zero is for the numerator to equal zero - no matter the value of the denominator. In the case of x(x+1)/x+4, either x=0 or x+1=0. So:

0(0+1)/0+4 = 0/4

 

or

 

x+1=0

x=0-1

x=-1

-1(0)/-1+4 = 0/3

 

So, x=-1 & x=0 will make the fraction equal zero.

 

 

Answer 2

Hi Kiranpreet,

 

If you set the numerator of the fraction equal to zero, you can then solve for x. The one exception is that the denominator cannot equal zero, because then it would be undefined. So:

 

x(x+1)=0

 

So here you are multiplying two numbers together, x and (x+1). If you multiply any number by zero, your answer will be zero. So you could say:

 

x=0   and  x+1=0

 

Therefore, x=0 and x=-1

 

Hope that makes sense! Let me know if you have any other questions!