Answer:
The simplified form is 1 over the quantity x plus 2 times the quantity
x minus 5 ⇒ 1/(x+2)(x-5) ⇒ last answer
Step-by-step explanation:
* Lets write the product of the two fraction
∵
- At first factorize the denominators
# x² - 3x - 10
∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the
2nd bracket
∵ -10 = 2 × -5 ⇒ 2nd term in the 1st bracket and 2nd term in the
2nd bracket
∵ x × - 5 = -5x ⇒ ext-reams
∵ x × 2 = 2x ⇒ means
∵ 2x + -5x = -3x ⇒ middle term
∴ x² - 3x - 10 = (x + 2)(x - 5)
# x² + x - 12
∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the
2nd bracket
∵ -12 = -3 × 4 ⇒ 2nd term in the 1st bracket and 2nd term in the
2nd bracket
∵ x × 4 = 4x ⇒ ext-reams
∵ x × -3 = -3x ⇒ means
∵ 4x + -3x = x ⇒ middle term
∴ x² + x - 12 = (x - 3)(x + 4)
* Lets write the fractions after factorization
∴
- lets simplify the fractions by cancel (x - 3) up with (x - 3) down
and cancel(x + 4) up with (x + 4) down
∴
* The simplified form is 1 over the quantity x plus 2 times the
quantity x minus 5