Thread: adding and subtracting rational expressions

a)4x+1/3x-5 + 2x/12x-20

b) 3x-1/x^2+4x+3 - x+6/2x^2+7x+1

Simplify and state restrictions on the variable
Please help

Originally Posted by euclid2

a)4x+1/3x-5 + 2x/12x-20

b) 3x-1/x^2+4x+3 - x+6/2x^2+7x+1

Simplify and state restrictions on the variable
Please help

(a) First factorise and cancel where possible

4x+1/3x-5 + 2x/12x-20 = 4x+1/3x-5 + 2x/4(3x-5) = 4x+1/3x-5 + x/2(3x-5)

Then multiply the top and bottom of each fraction so that they have the same denominator

= 2(4x+1)/2(3x-5) + 2x/4(3x-5)

Then add the fractions together

= (8x+2+2x)/2(3x-5) = (10x+2)/2(3x-5)

Finally factorise and cancel down if possible

= 2(5x+1)/2(3x-5) = (5x+1)/(3x-5)

(b) similar

what would be the restrictions or how do you get the restrictions?

Originally Posted by euclid2

what would be the restrictions or how do you get the restrictions?

The denominators in the individual fractions cannot be 0. Set each denominator equal to 0 and solve for x to see values of x that CANNOT be allowed.