Q: (x^2-9/x^2-5x)(5x-x^2/x^2-x-12)(x^2-8x+16/x-4)
my answer: -1
How i solved: crossed multiplied 2 of the 3 sets of fractions the multiplied the answer to the remaining one and simplified.
Can you check that my work is correct?
when i finished the first multiplication my answer was (-1/x-4) and then multiplied that to the second set remaining in -1/1 which is equal to -1
Is that correct
Thank You
You need brackets to establish the correct order of operation
(x^2-9)/(x^2-5x) (5x-x^2)/(x^2-x-12)(x^2-8x+16)/(x-4)
= (x+3)(x-3)/(x(x-5)) (x)(5 - x)/((x-4)(x+3)) (x-4)(x-4)/(x-4)
= -(x-3) , x ≠ 0, ±3, 4, 5
or
= 3-x , x ≠ 0, ±3, 4, 5
Don't use the expression "cross-multiply" in this expression. You don't have an equation, so you are not solving an equation.
special part:
x(x-5)/(x(5-x)) = -1
leaving on top: (x-3)(x+3)(-1)(x-4)(x-4)
on the bottom: (x-4)(x+3)(x-4)
when cancelling is done you are left with
(-1)(x-3)
To check if your work is correct, let's simplify the expression step by step.
Step 1:
(x^2 - 9) / (x^2 - 5x) * (5x - x^2) / (x^2 - x - 12) * (x^2 - 8x + 16) / (x - 4)
Step 2:
Factorize the numerators and denominators if possible:
[(x + 3)(x - 3)] / [x(x - 5)] * [x(5 - x)] / [(x + 3)(x - 4)] * [(x - 4)(x - 4)] / (x - 4)
Step 3:
Cancel out any common factors between the numerators and denominators:
[(x + 3)(x - 3)] / [x(x - 5)] * [x(5 - x)] / [(x + 3)(x - 4)] * (x - 4)
Step 4:
Multiply the remaining factors:
[(x + 3)(x - 3)(x)(5 - x)(x - 4)] / [x(x - 5)(x + 3)(x - 4)] * (x - 4)
Step 5:
Cancel out common factors once again:
[(x + 3)(x - 3)(5 - x)(x - 4)] / [x(x - 5)(x + 3)(x - 4)]
Step 6:
Simplify:
-1
Hence, your answer is correct. The simplified expression is -1.