Which of the following are equal to the rational expression below? x^2+x-6/x^2-2x-15

Hello from MrBillDoesMath!

(x-2)/(x-5)

Discussion:

Factor the numerator and denominator:

x^2 + x - 6 = (x+3)(x-2)

x^2-2x-15 =  (x+3)(x-5)

So  

( x^2 + x - 6) / x^2-2x-15  =   ( (x+3)(x-2) ) / ( (x+3)(x-5) )

Cancelling the (x+3) term in numerator and denominator gives

(x-2)/(x-5)

Regards,  

MrB

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

853.3

step-by-step explanation: