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solve 5/2x-4/x^2=7/2x^2

I need to know the steps and how to solve the rational equation.

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2 Answers

5/2x-4/x^2=7/2x^2, Solution: x=3

Step by Step

multiply by 4x^2 the whole expression. It is because 4x^2 is the common denominator between 2x,x,and 2x^2. To add fraccion they have to have common denominator.

4x^2[5/2x-4/x^2] = 4x^2[7/2x^2] ==> 

10x-16=14 ==> 

10x=14+16 ==> 

10x=30 ==> 

x=30/10 ==> 


     5/(2x) - 4/(x2) = 7/(2x2

First, set the equation equal to 0 by moving all the terms to one side of the equation. For simplicity, subtract 7/(2x2) from both sides of the equation:

     5/(2x) - 4/(x2) - 7/(2x2) = 0

Now we went to generate a least common denominator among all terms on the left hand side of the equation. Notice that 2x2 is the least common denominator here, so we want to manipulate all of the terms in a way such that they all have a denominator of 2x2. To do this, multiply the numerator and the denominator of the first term by x and multiply the numerator and the denominator of the second term by 2:

     5(x)/(2x)(x)  -  4(2)/(x2)(2)  -  7/(2x2)  =  0 

     5x/(2x2) - 8/(2x2) - 7/(2x2) = 0

Since all the terms now share a common denominator, we can add their numerators:

     (5x - 8 - 7)/(2x2) = 0

     (5x - 15)/(2x2) = 0

After we cross-multiply, we arrive at the following:

     5x - 15 = 0

Adding 15 to both sides of the equation we get the following:

     5x = 15

Divide both sides of the equation by 5 to solve for x:

      x = 3