## anonymous 4 years ago how do you solve 3/x+1 +2/x+3 =2? Please show me step by step. Thank you.

1. anonymous

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

2. anonymous

3. anonymous

$\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?

4. anonymous

let me see...

5. anonymous

Did you get it yet?

6. anonymous

7. anonymous

$3x + 9 + 2x + 2 = 2x^{2} + 8x + 6$$2x^{2} + 3x - 5 = 0$

8. anonymous

9. anonymous

yes.

10. anonymous

What did you get?

11. anonymous

i'm still doing it.

12. anonymous

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

13. anonymous

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$

14. anonymous

Do you see how I got that?

15. anonymous

yes.

16. anonymous