Question

Combine the following rational expressions
1/2y-5-30/8y^3-125
Lcm:(2y-5)(4y^2+10y+125)
=1*4y^2+10y+25/(2y-5)(4y^2+10y+25)-30/(2y-5)(4y^2+10y+25)
=4y^2-10y+25-30/(2y-5)(4y^2+10y+25)
=(4y^2+10y-5)/(2y-5)(4y^2+10y+25) Please correct my answer and I know it is wrong please explain the steps completely.

Answer 1

1/(2y-5) - 30/(8y^3-125)
1/(2y-5) - 30/((2y)^3 - 5^3)
1/(2y-5) - 30/((2y-5)(4y^2+10y+25))
The LCM is just (8y^3-125), so that gives

((4y^2+10y+25)-30)/(8y^3-125) = (4y^2+10y-5)/(8y^3-125)

Answer 2

actually, your answer is correct, despite the typo