SOLUTION: how would you factor out this rational function and find the domain, and simplify it to its lowest terms ? f(x)= 2x^2-10x/4x^2-100

Algebra ->  Rational-functions -> SOLUTION: how would you factor out this rational function and find the domain, and simplify it to its lowest terms ? f(x)= 2x^2-10x/4x^2-100      Log On


   

Question 537909: how would you factor out this rational function and find the domain, and simplify it to its lowest terms ?
f(x)= 2x^2-10x/4x^2-100
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%282x%5E2-10x%29%2F%284x%5E2-100%29 Factor an x from the numerator.
f%28x%29+=+x%282x-10%29%2F%284x%5E2-100%29 The denominator is the difference of squares and can be factored: A%5E2-B%5E2+=+%28A-B%29%28A%2BB%29.
f%28x%29+=+x%2Across%28%282x-10%29%29%2Fcross%28%282x-10%29%29%282x%2B10%29 = highlight%28x%2F%282x%2B10%29%29
Notice that if you were to substitute x+=+-5 in the denominator of the simplified solution, you would have division by zero, which is a no-no in math. Also note that if you were to substitute x+=+5 or x+=+-5 in the denominator of the given function, you would have division by zero, so x+=+5 and x+=+-5 are not allowed.
The domain (all allowable values of x) is all real numbers except 5 and -5.