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

Question

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

Answer 1

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 ==> 

x=3

Answer 2

     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