Question

Simplify completely x^2-100/x^2+2X-120 DIVIDED BY 6x+60/x-2

Answer 1

Factor out the GCF of 6 from each term in the polynomial.
((1)/(6(x)+6(10))*(x^(2)-100)/(x^(2)+2x-120))/(x-2)

Factor out the GCF of 6 from 6x+60.
((1)/(6(x+10))*(x^(2)-100)/(x^(2)+2x-120))/(x-2)

the binomial can be factored using the difference of squares formula, because both terms are perfect squares.

The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(((1)/(6(x+10))*((x-10)(x+10))/(x^(2)+2x-120)))/(x-2)

In this problem 12*-10=-120 and 12-10=2, so insert 12 as the right hand term of one factor and -10 as the right-hand term of the other factor
((1)/(6(x+10)*((x-10)(x+10))/((x+12)(x-10))))/(x-2)


Reduce the expression by canceling out the common factor of (x-10) from the numerator and denominator
(((1)/(6(x+10))*(1(x+10))/(x+12)))/(x-2)

Cancel the common factor of (x+10) from the denominator of the first expression and the numerator of the second expression
((1)/(6)*(1)/(x+12))/(x-2)

Multiply the rational expressions to get (1)/(6(x+12))
((1)/(6(x+12)))/(x-2)

Multiply the rational expressions to get
(1)/(6(x-2)(x+12))

Answer 2

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