Answer:
![x=-3](https://tex.z-dn.net/?f=x%3D-3)
Step-by-step explanation:
<u>Given equation</u>:
![\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7Bx%2B1%7D%2B%5Cdfrac%7B3%28x%2B1%29%7D%7Bx%7D%3D5)
Make the <u>denominators</u> the same:
![\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2x%7D%7Bx%2B1%7D%20%5Ccdot%5Cdfrac%7Bx%7D%7Bx%7D%2B%5Cdfrac%7B3%28x%2B1%29%7D%7Bx%7D%20%5Ccdot%20%5Cdfrac%7Bx%2B1%7D%7Bx%2B1%7D%3D5)
![\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2x%5E2%7D%7Bx%28x%2B1%29%7D%2B%5Cdfrac%7B3%28x%2B1%29%5E2%7D%7Bx%28x%2B1%29%7D%20%3D5)
<u>Combine</u> the fractions:
![\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B2x%5E2%2B3%28x%2B1%29%5E2%7D%7Bx%28x%2B1%29%7D%20%3D5)
<u>Multiply</u> both sides by x(x+1):
![\implies 2x^2+3(x+1)^2 =5x(x+1)](https://tex.z-dn.net/?f=%5Cimplies%202x%5E2%2B3%28x%2B1%29%5E2%20%3D5x%28x%2B1%29)
<u>Expand</u> the brackets:
![\implies 2x^2+3(x^2+2x+1) =5x^2+5x](https://tex.z-dn.net/?f=%5Cimplies%202x%5E2%2B3%28x%5E2%2B2x%2B1%29%20%3D5x%5E2%2B5x)
![\implies 2x^2+3x^2+6x+3 =5x^2+5x](https://tex.z-dn.net/?f=%5Cimplies%202x%5E2%2B3x%5E2%2B6x%2B3%20%3D5x%5E2%2B5x)
<u>Combine</u> like terms:
![\implies 5x^2+6x+3=5x^2+5x](https://tex.z-dn.net/?f=%5Cimplies%205x%5E2%2B6x%2B3%3D5x%5E2%2B5x)
<u>Subtract</u> 5x² from both sides:
![\implies 6x+3=5x](https://tex.z-dn.net/?f=%5Cimplies%206x%2B3%3D5x)
<u>Subtract</u> 5x from both sides:
![\implies x+3=0](https://tex.z-dn.net/?f=%5Cimplies%20x%2B3%3D0)
<u>Subtract</u> 3 from both sides:
![\implies x=-3](https://tex.z-dn.net/?f=%5Cimplies%20x%3D-3)
Learn more about algebraic fractions here:
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