Question

x + 3 / x +5 + x / 6 = 5 / 6

Answer 1

\[\frac{ x + 3 }{ x + 5 } + \frac{ x }{ 6 } = \frac{ 5 }{ 6 }\]

Answer 2

find some common denominators so you can add them together

Answer 3

6(x + 5)?

Answer 4

yes

Answer 5

What next?

Answer 6

\[\frac{ 6(x+3) }{ 6(x+5) }+\frac{ x(x+5) }{ 6(x+5) } = \frac{ 5(x+5) }{ 6(x+5) }\]

Answer 7

Then you cancel right?

Answer 8

so now you can just get rid of all the denominators, so:

6(x+3) + x(x+5) = 5(x+5)

Answer 9

Okay

Answer 10

so now just solve for x like a normal quadratic equation

Answer 11

Hold on one sec.

Answer 12

6x + 18 + x^2 + 5x = 5x + 25

Answer 13

Then,

Answer 14

then move it all on to one side, and solve the quadratic equation

Answer 15

x^2 + x - 7 = 0

Answer 16

Is that one correct?

Answer 17

x^2 +11x +18 = 5x + 25

which equals
x^2 + 6x - 7 = 0

Answer 18

you forgot there was an extra '5x' on the left side

Answer 19

oh, So then you factor the quadratic equation. hold on.

Answer 20

(x + 7)(x - 1) = 0

Answer 21

Is that correct?

Answer 22

looks right to me

so x = -7 and 1

Answer 23

Thanks!

Answer 24

you're welcome