What is 10 divided by x squared plus five x equals 3 divided by x minus 2 divided by x plus 5?

Answer 1

An equation.

Ohh - you wanted to solve it for x? You'll need to be a little more clear on the exact equation itself then. For example, did you mean:

10/x2 + 5x = 3/x - 2/x + 5

Or perhaps:

10/(x2 + 5x) = 3/x - 2/(x + 5)

Given the answerability of the latter interpretation, we'll assume that's the one you're looking for:

10/(x2 + 5x) = 3/x - 2/(x + 5)

We start by giving the two terms on the right a common factor:

10/(x2 + 5x) = 3(x + 5)/(x2 + 5x) - 2x/(x2 + 5x)

You'll notice that both sides of the equation have the same numerator, so we can eliminate that altogether (if a/c = b/c, then a = b):

10 = 3(x + 5) - 2x

Now we'll expand and simplify:

10 = 3x + 15 - 2x

3x - 2x = 10 - 15

x = -5