Question

Which expression is equivalent to x^2+7x+12 over x^2-x-12

Answer 1

B

Explanation:

Answer 2

Explanation:

Factorize the expression.

Sum = 7

Product = 12

Factors = 4 , 3

4 + 3= 7 & 4*3 = 12

x² + 7x + 12 = x² + 4x + 3x + 4*3

= x(x + 4) + 3(x + 4)

= (x + 4)(x + 3)

Sum = -1

Product = -12

Factors = (-4) , 3

(-4) + 3 = (-1) & (-4)*3 = -12

x² - x - 12 = x² - 4x + 3x - 4*3

= x(x - 4) +3(x - 4)

= (x -4)(x +3)

`\sf (x^(2)+7x+12)/(x^(2)-x-12)=((x+4)(x + 3))/((x -4 )(x + 3))\\\\\bf \text{(x +3) in the numerator and denominator will get cancelled}`

`=(x+4)/(x-4)`