simplify and state restrictions on the variable
a)4x+1/3x-5 + 2x/12x-20
b)3x-1/x^2+4x+3 - x+6/2x^2+7x+1
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simplify and state restrictions on the variable
a)4x+1/3x-5 + 2x/12x-20
b)3x-1/x^2+4x+3 - x+6/2x^2+7x+1
a)4x+1/3x-5 + 2x/12x-20
For this one, I would reduce second fraction by multiplying by (1/2)/(1/2), which is essentially multiplying by 1, so it is allowed:
(4x+1)/(3x-5) + x/(6x-10)
Now, in order to get a common denominator, we have to multiply the first fraction by 2/2 to get the lcd of 6x-10:
(8x+2)/(6x-10) + x/(6x-10)
Now, we can add the numerators because both fractions have the same denominator:
(8x+2+x)/(6x-10)
which becomes:
(9x+2)/(6x-10)
I don't think this could be reduced anymore.
Oh yeah, 6x-10 cannot equal zero because then it would cause the fraction to have a zero in the denominator.
So, we solve 6x-10 = 0 to get:
6x=10
x=10/6 Reduce
x=5/3
So, for this problem, x cannot equal 5/3.