Question

How do I solve this? Please show steps clearly so i can understand, thank you

Answer 1

Answer:

The value of $x=8$.

Step-by-step explanation:

Given:

$\frac{x+3}{x}-\frac{x+1}{x+4}=\frac{5}{x}$

We need to solve this equation.

Solution:

First combining equation having same denominators we get;

$\frac{x+3}{x}-\frac{5}{x}=\frac{x+1}{x+4}$

Now denominators are common so we will solve the numerators we get;

$\frac{x+3-5}{x}=\frac{x+1}{x+4}\\\\\frac{x-2}{x}=\frac{x+1}{x+4}$

Now by cross multiplication we get;

$(x-2)(x+4)=x(x+1)$

Now Applying distributive property we get;

$x^2+4x-2x-8=x^2+x\\\\x^2+2x-8=x^2+x$

Now Combining the like terms we get;

$x^2+2x-x^2-x=8\\\\x=8$

Hence on solving we get the value of $x=8$.