SOLUTION: Simplify: (x / 2x^2-7x+3) - ((x-4) / (2x-1)(3-x)) - (7 / (x^2-x-6))

Algebra ->  Real-numbers -> SOLUTION: Simplify: (x / 2x^2-7x+3) - ((x-4) / (2x-1)(3-x)) - (7 / (x^2-x-6))      Log On


   

Question 1189175: Simplify: (x / 2x^2-7x+3) - ((x-4) / (2x-1)(3-x)) - (7 / (x^2-x-6))
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let's factor the denominators and do a bit of tidying up.

x%2F%282x%5E2-7x%2B3%29+-+%28x-4%29+%2F%28%282x-1%29%283-x%29%29+-+7+%2F+%28x%5E2-x-6%29







%28x+%2B+%28x-4%29%29+%2F%28%282x-1%29%28x-3%29%29+-+7+%2F+%28%28x-3%29%28x%2B2%29%29

%282x-4%29+%2F%28%282x-1%29%28x-3%29%29+-+7+%2F+%28%28x-3%29%28x%2B2%29%29

When focusing on the denominators, the unique factors are: (2x-1), (x-3), (x+2)
The LCD is therefore (2x-1)(x-3)(x+2)
Let's get each denominator to be equal to the LCD. That way we can add the fractions.

%282x-4%29+%2F%28%282x-1%29%28x-3%29%29+-+7+%2F+%28%28x-3%29%28x%2B2%29%29







%282x%5E2-8+-+%2814x-7%29+%29%2F+%28%282x-1%29%28x-3%29%28x%2B2%29%29

%282x%5E2-8+-+14x%2B7+%29%2F+%28%282x-1%29%28x-3%29%28x%2B2%29%29

%282x%5E2+-+14x-1+%29%2F+%28%282x-1%29%28x-3%29%28x%2B2%29%29

%282x%5E2+-+14x-1+%29%2F+%28%282x-1%29%28x%5E2-x-6%29%29

%282x%5E2+-+14x-1+%29%2F+%282x%28x%5E2-x-6%29-1%28x%5E2-x-6%29%29

%282x%5E2+-+14x-1+%29%2F+%282x%5E3-2x%5E2-12x-x%5E2%2Bx%2B6%29

%282x%5E2+-+14x-1+%29%2F+%282x%5E3-3x%5E2-11x%2B6%29

--------------------------------------------

Answer: The original expression simplifies fully to %282x%5E2+-+14x-1+%29%2F+%282x%5E3-3x%5E2-11x%2B6%29