SOLUTION: If f(x)= 3x^2 -27/ 18x + 30 and g(x) = x^2 -7x +12/ 3x^2 -7x -20 , find f(x) divided by g(x) for all values of x for which the expression is defined and express your answer in simp

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If f(x)= 3x^2 -27/ 18x + 30 and g(x) = x^2 -7x +12/ 3x^2 -7x -20 , find f(x) divided by g(x) for all values of x for which the expression is defined and express your answer in simp      Log On


   

Question 197213: If f(x)= 3x^2 -27/ 18x + 30 and g(x) = x^2 -7x +12/ 3x^2 -7x -20 , find f(x) divided by g(x) for all values of x for which the expression is defined and express your answer in simplest form. Help is appreciated! Thank you!
Solution:
f(x)=%283x%5E2+-27%29%2F%2818x+%2B+30+%29------(1)
g(x) = %28x%5E2+-7x+%2B12%29%2F%283x%5E2+-7x+-20%29 ------(2)
f(x)/g(x)==> f(x)*(1/g(x))
==> %28%283x%5E2-27%29%2F%2818x%2B30%29%29%2A%28%283x%5E2-7x-20%29%2F%28x%5E2-7x%2B12%29%29
==> 3%28x%5E2-9%29%2F6%283x%2B5%29%2A%28%283x%2B5%29%28x-4%29%29%2F%28%28x-4%29%28x-3%29%29
==>
==>
==>
==>
==> %28%28x%2B3%29%2Ahighlight%28%283x%2B5%29%29%29%2F%282highlight%28%283x%2B5%29%29%29
==> %28%28x%2B3%29%2Across%28%283x%2B5%29%29%29%2F%282cross%28%283x%2B5%29%29%29
So the simplest form is %28x%2B3%29%2F2
Found 2 solutions by stanbon, mathsteacher:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If f(x)= 3x^2 -27/ 18x + 30 and g(x) = x^2 -7x +12/ 3x^2 -7x -20 , find f(x) divided by g(x) for all values of x for which the expression is defined and express your answer in simplest form. Help is appreciated! Thank you!
-----
f(x) = [3(x-3)(x+3)]/[6(3x+5)]
---------------------------------
g(x) = [(x-3)(x-4)]/[3x^2 -12x + 5x - 20]
= [(x-3)(x-4)]/[(x-4)(3x+5)]
--------------------
Cancel the factors that are common to a numerator and a denominator to get:
f(x)/g(x) = [(x+3)/2/[1/1]
---
f(x)/g(x) = [(x+3)/[2]
========================================
Cheers,
Stan H.

Answer by mathsteacher(28) About Me  (Show Source):