For division and multiplication, there is a rule that we can cross-cancel terms that appear in both the top and bottom of a fraction. By applying this rule to the above equation the `(x - 3)` terms and `(x - 2)` terms in the numerator and the denominator will cross-cancel each other.
Then, we can simplify the equation as `(x+2)/(x+5)`. This is the simplification of the original expression.
Note: To these results, there are certain restrictions on `x`. `x±2` and `x=-5` should be excluded beforehand as these values will result in a zero in the denominator of the original expression.
Answers & Comments
Answer:
(x+2)/(x+5)
Step-by-step explanation:
First, let's note that our expression
(x²- 3x) / (x² + 3x - 10) * (x² - 4) / (x² - x - 6)
is the multiplication of two fractions (rational functions).
For the sake of simplification, let's factorize every polynomial in each numerator and denominator.
The factorization would look like:
Numerator of the first fraction: `x² - 3x = x(x - 3)`
Denominator of the first fraction: `x² +3x -10 = (x - 2)(x + 5)`
Numerator of the second fraction: `x² - 4 = (x - 2)(x + 2)`
Denominator of the second fraction: `x² -x -6 = (x - 3)(x + 2)`
Substitute these factorisations into the original expression, we get:
(x(x - 3)) / ((x - 2)(x + 5)) * ((x - 2)(x + 2)) / ((x - 3)(x + 2))
For division and multiplication, there is a rule that we can cross-cancel terms that appear in both the top and bottom of a fraction. By applying this rule to the above equation the `(x - 3)` terms and `(x - 2)` terms in the numerator and the denominator will cross-cancel each other.
Then, we can simplify the equation as `(x+2)/(x+5)`. This is the simplification of the original expression.
Note: To these results, there are certain restrictions on `x`. `x±2` and `x=-5` should be excluded beforehand as these values will result in a zero in the denominator of the original expression.