# How do you solve #x+(x+5)/(x-7)=(10x-58)/(x-7)# and check for extraneous solutions?

##### 1 Answer

9; read below for extraneous

#### Explanation:

First of all, seeing how this question deals with fractions, multiply the value of

Now we have three fractions with the same denominator:

Because the denominators are all the same, they eventually cancel out by cross-multiplication, so we can drop them to get a simple equation:

At this point, it is a matter of combining like terms and simplifying for an answer

=>

=>

=>

Now we have two answers, and the problem seems over, right? Well, it isn't, as we have an extraneous solution: 7. This is because, when plugged back into the original equation, 7 creates a denominator of 0; dividing by zero is impossible, so we exclude 7 as a possible answer. So we are left with one final answer: 9