Question

I was looking on a website that teaches linear algebra and it had this problem:

3x - 15
_______ =0

2x + 1

And it says the answer is: x = 5

But I don't understand how to get that answer so I hope someone can give me step by step directions for it.

Answer 1

As long as x≠-1/2, the denominator is not zero. In that case, the only way for the expression to be zero is when the numerator becomes zero, or
3x-15=0, which gives x=5 as the root.

In the case when x=-1/2, the expression becomes undefined, and no solution is possible.