What is x minus 3 over x^2 minus 25 over x^2 minus 9 over x minus 5?
Mathematics · High School · Tue Nov 03 2020
Answered on
Given the statement:
x minus 3 over x^2 minus 25 over x^2 minus 9 over x minus 5
Representation:
The statement can be written as,
((x -3)/ (x^2 -25))/((x^2 -9)/(x -5))
Solution:
In order to solve the fraction, we take the reciprocal of the denominator ((x^2 -9)/(x -5)), and multiply it with the numerator.
=((x -3)/ (x^2 -25)) ((x -5 )/(x^2 - 9))
= ((x-5)(x-3))/((x^2-25)(x^2-9))
The denominator can be expanded since it is the sum and difference of two squares.
= ((x-5)(x-3))/((x-5)(x+5)(x-3)(x + 3))
(x -5)(x-3) cancels, leaving behind,
= 1/(x + 5)(x +3)
Use the FOIL Method in order to simplify the denominator.
x^2 + 3x + 5x + 15
x^2 + 8x + 15
= 1/(x^2 + 8x +15)
Final answer:
= 1/(x^2 + 8x +15)