### 3 Answers

(y – 1)/(y^2 + y – 6) / ((y – 6)/(y + 3))

= (y – 1)/((y + 3)(y – 2)) / ((y – 6)/(y + 3))

= (y – 1)/((y – 2)(y – 6))

Break the complex fraction up into division:

(y – 1) / (y^2 + y – 6) Ã· (y – 6) / (y + 3)

Factor out as much as possible:

(y – 1) / (y + 3)(y – 2) Ã· (y – 6) / (y + 3)

Like you would in normal fractional divison, flip the second fraction and multiply:

(y – 1) / (y + 3)(y – 2) x (y + 3) / (y – 6)

When multiplying fractions you can simplify either vertically or diagonally, NEVER horizontally. So simplify the (y + 3) and (y + 3):

(y – 1) / (y – 2) x 1 / (y – 6)

Now multiply the numerators and denominators into each other:

(y – 1) / (y – 2)(y – 6)

Note that brackets MUST be used.

(y – 1) / (yÂ² + y – 6)

—————————

(y – 6) / (y + 3)

(y – 1) (y + 3)

———————–

(y – 6) (y + 3)(y – 2)

y – 1

—————-

(y – 6) (y – 2)