Question 1187375: Simplify each of the following and state any restrictions on the variable.
(4x+1)/(3x-5) + (2x)/(12x-20)
(3x-1)/(x^2+4x+3) - (x+6)/(x^2+7x+12)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! multiply the first term by 4/4
4(4x+1) divided by 4(3x-5) (which is 12x-20) add 2x/(12x-20)
The difference between the numerators is 16x+4+2x=18x+4
The answer is (18x+4)/(12x-20)
(9x+2)/6x-10), so long as x does not equal (10/6) or (5/3)
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This is
(3x-1)/(x+1)(x+3) subtract (x+6)/(x+4)(x+3)
common denominator is (x+1)(x+3)(x+4) which will cover every term in each.
multiply the first by (x+4)/(x+4), so the product is (3x-1)(x+4)=3x^2+11x-4 divided by the common denominator.
multiply the second term by (x+1) so it is x^2+7x+6 divided by the common denominator.
subtract the second numerator from the first to get 2x^2+4x-10 divided by the common denominator.
This is 2(x^2+2x-5)/(x+1)(x+4)(x+3). Restrictions: x cannot be -1, -4, or -3.
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