y+7/y-4+3/y-4

Question

How to solve this equation i'm trying to find out what y is ?

 

Answer 1

The way you've typed this problem doesn't make much sense. First, note that this is an expression and not an equation since it is not set equal to anything. Second, you need to use parentheses in order to distinguish which denominator belongs to which numerator.

Let's assume the rational expression is as follows:     ((y+7)/(y-4)) + ((3)/(y-4))

This rational expression has two fractional terms. The first term has a numerator of y+7 and a denominator of y-4, while the second term has a numerator of 3 and a denominator of y-4. Since the two fractional terms in the expression have the same denominator, we can add their numerators and keep the like denominator. That is,

     ((y+7)/(y-4)) + ((3)/(y-4)) = ((y+7)+(3))/(y-4) = (y+7+3)/(y-4) = (y+10)/(y-4)

Recall that when dealing with fractions their denominators cannot equal 0 because anything divided by 0 is undefined. This applies to rational expressions as well since they contain polynomial fractions. You cannot solve for y here since this is an expression and not an equation, however, you can solve for what y is not. That is, y can essentially be equal to anything as long as the denominator does not equal 0. So we can find for which y-values the denominator will equal 0 and these values are what y cannot equal in the expression. Therefore, for the following expression

          (y+10)/(y-4)

     set the denominator equal to 0 and solve for y:

               y - 4 = 0          (add 4 to both sides of the equation)

               y - 4 + 4 = 0 + 4

               y = 4

This means that when y equals 4 the denominator will be 0, which is undefined.

Thus, the solution for y in this expression is all real numbers y except y=4.