Question

The png is attached please help:)) you have to find the quotient

Answer 1

Answer: x=2, and cannot be equal to -5, -2 or 0

Explanation:

Basically, (x^2+7x+10)=(x+2)(x+5)

The denominator cannot be 0, so it cannot be equal to -5 or -2

It also obviously cannot be 0, or else the second part would be equal to 0, and the problem would be invalid.

From noticing that 3x+15=3(x+5), we can change the equation to
(6x/3)/(x^2+2x)/(x+2)

Simplifying it further, we get that x^2+2x=x(x+2)

(6x/3)/x

6/3

2

Answer 2

2, -5, 0, -2

Explanation:

Equation is 6x/3x+15 divided by x^2+2x/x^2+7x+10
Multiply the first equation by the reciprocal of second

6x/3x+15 * x^2+7x+10/x^2+2x
Find the quotient by dividing:

2x/x+5 * x^2+7x+10/x^2+2x
Factor out x^2+7x+10

2x/x+5 * (x+2)(x+5)/x^2+2x
Simplify to

2
x cannot equal to -5, 0, -2 because:

no denominator can equal 0

if x = -5: 2x/x+5 = 2x/0

if x = 0: (x+2)(x+5)/x^2+2x = (x+2)(x+5)/0

if x = -2: (x+2)(x+5)/x^2+2x= (x+2)(x+5)/0