Simplify the expressions in each pair. (2 marks each) (Show your work)
(x^2-2x)/(x+1)x (x^2-1)/(x^2+x-6)
My work on simplifying the expressions
x(x-2)/x+1 x (x+1)(x-1)/(x+3)(x+2)
If I've gone wrong please help me understand where I went wrong and help me get the correct answer.
Sincerely, yours
Alex Hunter
(x�0…5-2x)/(x 1)x (x�0…5-1)/(x�0…5 x-6)
= x(x-2)/x 1 x (x 1)(x-1)/(x 3)(x-2)
=X/1 x (x-1)/(x 3)
=x(x-1)/(x 3)
Well hope its helpful.
yours (x^2-2x)/(x+1)x (x^2-1)/(x^2+x-6)
My work on simplifying the expressions
x(x-2)/(x+1) * (x+1)(x-1)/[(x+3)(x-2)]
note your sign error in second denominator
(x+1) and (x-2) cancel
x(x-1) / (x+3)
To simplify the expressions, we need to factorize the numerators and denominators. Let's start with the first expression:
(x^2 - 2x)/(x + 1)x
First, let's factorize the numerator:
x^2 - 2x = x(x - 2)
The denominator is already factored.
Now, let's simplify the second expression:
(x^2 - 1)/(x^2 + x - 6)
The numerator can be factored as the difference of squares:
x^2 - 1 = (x + 1)(x - 1)
The denominator can be factored by finding two numbers whose product is -6 and whose sum is +1:
x^2 + x - 6 = (x + 3)(x - 2)
Now, let's rewrite the expressions:
(x^2 - 2x)/(x + 1)x = (x(x - 2))/((x + 1)x)
(x^2 - 1)/(x^2 + x - 6) = ((x + 1)(x - 1))/((x + 3)(x - 2))
To simplify further, we can cancel out the common factors:
(x(x - 2))/((x + 1)x) = (x - 2)/(x + 1)
((x + 1)(x - 1))/((x + 3)(x - 2)) = (x - 1)/(x + 3)
So, the simplified expressions are:
(x - 2)/(x + 1)
(x - 1)/(x + 3)
I hope this helps! If you have any further questions or need additional assistance, feel free to ask.