How do you divide #(\frac { 9x ^ { 2} - 13x - 10} { x ^ { 2} - x - 6} ) \div ( \frac { 3x ^ { 2} - 2x - 8} { x ^ { 2} + x - 6} ) #?

1 Answer
marfre
Apr 18, 2017

#((9x + 5)(x-2)(x+3))/((x+2)(x-3)(3x+4))#

Explanation:

Dividing a fraction by a fraction is the same thing as multiplying the first fraction by the reciprocal of the second fraction. This holds true also for polynomials.

# (9x^2 - 13x - 10)/(x^2 - x - 6) -: (3x^2 - 2x - 8)/(x^2 + x - 6)#

# = (9x^2 - 13x - 10)/(x^2 - x - 6) * (x^2 + x - 6)/(3x^2 - 2x - 8)#

Factor each polynomial:

# = ((9x + 5)(x-2))/((x+2)(x-3)) * ((x+3)(x-2))/((x-2)(3x+4))#

Now cancel any term that is found in both the numerator and denominator:

# = ((9x + 5)(x-2))/((x+2)(x-3)) * ((x+3)cancel(x-2))/(cancel(x-2)(3x+4))#

#= ((9x + 5)(x-2)(x+3))/((x+2)(x-3)(3x+4))#

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