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solve for x : \(\frac{3x^2+2x+1}{x-1}=3x+1\)

tertre  Mar 5, 2017
 #1
avatar+7155 
+6

Follow the exact same steps that you needed to do for the other problems. I will try to explain the steps super good so that you can do more problems like this on your own. :)

\(\frac{3x^2+2x+1}{x-1} = 3x + 1\)

 

Multiply both sides by (x-1):

\((\frac{3x^2+2x+1}{x-1})(x-1) = (3x + 1)(x-1)\)

 

Multiply out the right side. A lot of teachers teach it with the acroynm FOIL. It just means that you have to multiply each thing in the first set of parenthesees by each thing in the second set of parenthesees and add each product together.

\(3x^2+2x+1 = 3x(x) + 3x(-1) + 1(x) + 1(-1)\)

 

Multiply:

\(3x^2+2x+1 = 3x^2 - 3x + x - 1\)

 

Subtract 3x2 from both sides:

\(2x+1 = - 3x + x - 1\)

 

Subtract 2x from both sides:

\(1 = - 3x + x - 1 - 2x\)

 

Combine like terms:

\(1 = - 4x - 1\)

 

Add one to both sides:

\(2 = - 4x\)

 

Divide both sides by -4:

\(-\frac{1}{2} = x\)

hectictar  Mar 5, 2017

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