Question

solve for x: (4/x+1)-(1/2)=1/3x+3

Answer 1

\[\frac{ 4 }{ x+1 } - \frac{ 1 }{ 2 } = \frac{ 1 }{ 3x+3 }\]

Answer 2

You will need to find a common denominator for the 3 fractions

Answer 3

\[\frac{ 4(2)(3x+3) }{ 2(x+1)(3x+3 } - \frac{ 1(x+1)(3x+3) }{ 2(x+1)(3x+3) } = \frac{ 1(x+1)(2) }{ 2(x+1)(3x+3) }\]

Answer 4

So since the denominators are the same, we can subtract. I'll simplify the #s. So 24x+24 -
\[(24x+24)-(3x^2+6x+3)\]

Answer 5

Since we're subtraction, we will multiply (3x^2 + 6x+3) by -1 to get -3x^2-6x-3, now we will combine.

Answer 6

\[-3x^2 + 18x + 21 = 2x + 2\]

Answer 7

Now move the the numbers on the right to the left and equal it to 0. \[-3x^2 +16x + 19 = 0\]

Answer 8

Now use the Quadratic formula for your answer.

Answer 9

x = -1 and x = 19/3, But only x = 19/3 will work because if you we're to plug in x = -1, you would find out that it would turn out undefined.