3t^2-t over 6t^2 + 15t divided by 6t^2 + t - 1 over 2t^2 - 5t - 25?

Question

can somone please help me do the steps to this problem.

Answer 1

Step 1: Write it out.
(3t^2 - t) / (6t^2 + 15t) ÷ (6t^2 + t - 1) / (2t^2 - 5t - 25)

Step 2: Convert division to multiplication, by flipping the second fraction.
(3t^2 - t) / (6t^2 + 15t) * (2t^2 - 5t - 25) / (6t^2 + t - 1)

Step 3: Simplify the first fraction by cancelling out t, and factor the second fraction.
(3t - 1) / 3(2t + 5) * (2t + 5) (t - 5) / (3t - 1)(2t + 1)

Step 4: Multiply out the fractions, then cancel.
(3t - 1) (2t + 5) (t - 5) / 3 (3t - 1) (2t + 1) (2t + 5)
(t - 5) / 3 (2t + 1)

Step 5: Rewrite as fraction:
(t - 5) / (6t + 3) - solution