Answer:
The value of [tex]x=8[/tex].
Step-by-step explanation:
Given:
[tex]\frac{x+3}{x}-\frac{x+1}{x+4}=\frac{5}{x}[/tex]
We need to solve this equation.
Solution:
First combining equation having same denominators we get;
[tex]\frac{x+3}{x}-\frac{5}{x}=\frac{x+1}{x+4}[/tex]
Now denominators are common so we will solve the numerators we get;
[tex]\frac{x+3-5}{x}=\frac{x+1}{x+4}\\\\\frac{x-2}{x}=\frac{x+1}{x+4}[/tex]
Now by cross multiplication we get;
[tex](x-2)(x+4)=x(x+1)[/tex]
Now Applying distributive property we get;
[tex]x^2+4x-2x-8=x^2+x\\\\x^2+2x-8=x^2+x[/tex]
Now Combining the like terms we get;
[tex]x^2+2x-x^2-x=8\\\\x=8[/tex]
Hence on solving we get the value of [tex]x=8[/tex].
