Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)...

Question

Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]

Accepted Answer

Hello today we're going to go ahead and simplify a rational expression. The rational expression given to us is two X minus six over x squared minus four. And we're gonna be subtracting x minus four over x squared minus four. So one thing to notice about both of these fractions. Both of the denominators are the same. That means we can go ahead and combine this into a single fraction. Doing so is going to give us two x minus six minus the quantity x minus four and all of that is going to be over x squared minus four. Now we need to go ahead and simplify our numerator and denominator and we're gonna go ahead and start with the numerator paying attention to the numerator. We need to go ahead and open up this parentheses here that means we're gonna take our negative sign and distribute it to every term in the parentheses. Doing so is going to give me two x minus six minus X plus four. Now I can go ahead and combine like terms, combine the two X with the negative X. Is just going to give me X. And combining negative six with positive four is going to give me negative two. Now we need to go ahead and simplify the denominator. If you notice this is a difference of squares meaning that it is factory ble recall the difference of squares where you have a squared minus B squared and that is going to factor two A plus B times a minus B. In this case here are A is going to be X squared and r B is going to be four. So we can factor the denominator two, x plus two times x minus two. Now putting everything together, we are now going to have x minus two over X plus two times x minus two. And we can simplify this even further because we have an x minus two in the numerator and denominator, so we can go ahead and cancel out those quantities and that's going to leave us with one over X plus two. And that would be the simplest form of this equation. That means that the solution is going to be D. So I hope this helps you simplify rational equations and I'll go ahead and see you all in the next video.

Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]

Key Concepts

Common Denominator

Factoring Polynomials

Simplifying Rational Expressions

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