Nigel Emard
Feb 12, 2025
simplify the complex fraction. y -1/ y2 + y -6 over y-6/y+3?
Simplify the following complex fraction:
[ \frac{\frac{y - 1}{y^2 + y - 6}}{\frac{y - 6}{y + 3}} ]
What is the simplified result?
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) ÷ (y – 6) / (y + 3)
Factor out as much as possible:
(y – 1) / (y + 3)(y – 2) ÷ (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)
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