Thread: please help with rational expressions

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.