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Multiplication of Rational Functions
How to multiply rational functions:
(x + 1)/(x + 3) TIMES (2x + 3)/(x - 1)
I will multiply the numerators first.
(x + 1) (2x + 3) = 2x^3 + 5x + 3
I will now multiply the denominators.
(x + 3) ( x - 1) = x^2 + 2x -3
Final answer: 2x^3 + 5x + 3/x^2 + 2x - 3
x^2 - 4/x - 3 TIMES x^2 - 7x + 12/x^2 - 2x
1) Factor where needed.
(x + 2) (x - 2)/x - 3 and (x - 3) ( x - 4)/x(x - 2)
2) Cancel where you can.
We can cancel the following: (x - 3) with (x - 3) and (x - 2) with (x - 2).
After doing so, we are left with the final answer: (x + 2) ( x - 4)/x
You can leave the final answer as shown above (called factored form) or you can write your final answer in standard form by multiplying to simplify.
Look at the difference:
Factored Form For Sample B
(x + 2) ( x - 4)/x
Standard Form For Sample B
x^2 - 2x - 8/x
By Mr. Feliz