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.