Question

how do you solve 3/x+1 +2/x+3 =2? Please show me step by step. Thank you.

Answer 1

\[\text{Is this the question?}\frac3{x + 1} + \frac{2}{x + 3} = 2\]

Answer 2

yes please.

Answer 3

\[\frac3{x + 1} + \frac{2}{x + 3} = 2\]\[\frac{3}{x + 1} \times \frac{x + 3}{x + 3} + \frac{2}{x + 3} \times \frac{x + 1}{x + 1} = \frac{2}{1} \times \frac{(x + 1)(x + 3)}{(x + 1)(x + 3)}\]\[\frac{3(x + 3) + 2(x + 1)}{x^{2} + 4x + 3} = \frac{ 2(x^{2} + 4x + 3)}{x^{2} + 4x + 3}\]You can just drop the denominator now.
\[3(x + 3) + 2(x + 1) = 2(x^{2} + 4x + 3)\]Can you solve it now?

Answer 4

let me see...

Answer 5

Did you get it yet?

Answer 6

the next step please?

Answer 7

\[3x + 9 + 2x + 2 = 2x^{2} + 8x + 6\]\[2x^{2} + 3x - 5 = 0\]

Answer 8

Can you solve the quadratic?

Answer 9

yes.

Answer 10

What did you get?

Answer 11

i'm still doing it.

Answer 12

\[3\pm i \sqrt{31} \over 4\] is that right?

Answer 13

No.
\[3x + 9 + 2x + 2 = 2x^{2} + 8x + 6\]\[2x^{2} + 3x - 5 = 0\]\[2x^{2} -2x + 5x - 5 = 0\]\[2x(x - 1) + 5(x - 1) = 0\]\[(2x + 5)(x - 1) = 0\]\[x = -\frac{5}{2}, 1\]

Answer 14

Do you see how I got that?

Answer 15

yes.

Answer 16

thank you for your help.

Answer 17

np :)