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## kitsune0724 2 years ago how do you solve 3/x+1 +2/x+3 =2? Please show me step by step. Thank you.

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1. Calcmathlete

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

2. kitsune0724

yes please.

3. Calcmathlete

$\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. kitsune0724

let me see...

5. Calcmathlete

Did you get it yet?

6. kitsune0724

the next step please?

7. Calcmathlete

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

8. Calcmathlete

Can you solve the quadratic?

9. kitsune0724

yes.

10. Calcmathlete

What did you get?

11. kitsune0724

i'm still doing it.

12. kitsune0724

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

13. Calcmathlete

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. Calcmathlete

Do you see how I got that?

15. kitsune0724

yes.

16. kitsune0724

thank you for your help.

17. Calcmathlete

np :)

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