[(x^2-1)/(x-3)] / [(x^2-x-2)/(3x-9)]
I get (3x-3/x-2)
correct if you type it as
(3x-3)/(x-2)
Are you learning about restrictions?
since you divided out (x-3) and (x+1) , those two expressions cannot be zero
so the preferred answer would be
(3x-3)/(x-2) , x ≠1,2
(-3.6)0
To simplify the given expression, you can simplify each fraction individually and then divide the resulting fractions. Let's go step by step:
1. Simplify the first fraction: (x^2-1)/(x-3).
- This fraction cannot be simplified further as both the numerator and denominator are quadratic expressions.
2. Simplify the second fraction: (x^2-x-2)/(3x-9).
- This fraction can be factored:
Numerator: (x^2-x-2) = (x-2)(x+1)
Denominator: (3x-9) = 3(x-3)
- Cancel out the common factor of (x-3), leaving:
(x-2)/(3)
3. Divide the first fraction by the second fraction:
- Dividing by a fraction is the same as multiplying by the reciprocal of that fraction. Therefore, we can rewrite the expression as:
(x^2-1)/(x-3) * (3/(x-2))
- Multiply the numerators and denominators:
(x^2-1) * 3 / ((x-3) * (x-2))
- Simplify the numerator:
(x^2-1) * 3 = 3(x^2-1) = 3x^2 - 3
- Simplify the denominator:
(x-3) * (x-2) = x^2 - 2x - 3x + 6 = x^2 - 5x + 6
- The final simplified expression is:
(3x^2 - 3) / (x^2 - 5x + 6), which cannot be simplified further.
Therefore, the simplified expression is (3x^2 - 3) / (x^2 - 5x + 6). The expression you provided, (3x-3/x-2), is not equivalent to the original expression.