# Mathematics - Algebra

Choose one of the concepts for rational expressions from Chapter 6 that helps you to solve an equation with a rational expression. Attempt to explain this concept to the class in your own words, tell why it is important when attempting to solve an equation with a rational expression, then give an example. Use the problem below.

Reduce to lowest terms.....(see attachment for complete description)

w^2-49

_______

w + 7

https://brainmass.com/math/basic-algebra/mathematics-rational-expressions-205020

## SOLUTION This solution is **FREE** courtesy of BrainMass!

The solution file is attached.

Choose one of the concepts for rational expressions from Chapter 6 that helps you to solve an equation with a rational expression. Attempt to explain this concept to the class in your own words, tell why it is important when attempting to solve an equation with a rational expression, then give an example. Use the problem below.

Reduce to lowest terms.

43.

The given expression is called a rational expression because both numerator and denominator are polynomials. It should be noted that a rational expression is not defined for those values of the variable that make the denominator 0. Thus, the expression (w^2 - 49)/(w + 7) is defined only when w + 7 ¹ 0, that is, when w ¹ -7.

To simplify a rational expression, we attempt to factorize the numerator and the denominator so that common factors, if any, can be canceled.

Now, w^2 - 49 = w^2 - 7^2 = (w + 7)(w - 7)

(w^2 - 49)/(w + 7) = [(w + 7)(w - 7)]/(w + 7)

= w - 7 [Canceling the common (w + 7) term]

Thus, the given expression simplifies to w - 7 and this is the answer.

Another example:

Simplify (x^2 - 9x + 8)/(x^2 - 8x)

Solution:

x^2 - 9x + 8 = x^2 - x - 8x + 8 = x(x - 1) - 8(x - 1) = (x - 1)(x - 8)

x^2 - 8x = x(x - 8)

(x^2 - 9x + 8)/(x^2 - 8x) = [(x - 1)(x - 8)] / [x(x - 8)] = (x - 1)/x.

https://brainmass.com/math/basic-algebra/mathematics-rational-expressions-205020