anonymous
  • anonymous
how do you solve 3/x+1 +2/x+3 =2? Please show me step by step. Thank you.
Mathematics
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anonymous
  • anonymous
how do you solve 3/x+1 +2/x+3 =2? Please show me step by step. Thank you.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\text{Is this the question?}\frac3{x + 1} + \frac{2}{x + 3} = 2\]
anonymous
  • anonymous
yes please.
anonymous
  • 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?

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anonymous
  • anonymous
let me see...
anonymous
  • anonymous
Did you get it yet?
anonymous
  • anonymous
the next step please?
anonymous
  • anonymous
\[3x + 9 + 2x + 2 = 2x^{2} + 8x + 6\]\[2x^{2} + 3x - 5 = 0\]
anonymous
  • anonymous
Can you solve the quadratic?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
What did you get?
anonymous
  • anonymous
i'm still doing it.
anonymous
  • anonymous
\[3\pm i \sqrt{31} \over 4\] is that right?
anonymous
  • anonymous
No. \[3x + 9 + 2x + 2 = 2x^{2} + 8x + 6\]\[2x^{2} + 3x - 5 = 0\]\[2x^{2} -2x + 5x - 5 = 0\]\[2x(x - 1) + 5(x - 1) = 0\]\[(2x + 5)(x - 1) = 0\]\[x = -\frac{5}{2}, 1\]
anonymous
  • anonymous
Do you see how I got that?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
thank you for your help.
anonymous
  • anonymous
np :)

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