Answer:
x = 0 and x = 13
Step-by-step explanation:
[tex]\frac{2}{x+2}+\frac{1}{5}=\frac{6}{x+5}[/tex]
[tex]\frac{12+x}{5*(x+2)} =\frac{6}{x+5}[/tex]
- multiplying both sides by 5:
[tex]\frac{12+x}{x+2}=\frac{30}{x+5}[/tex]
[tex]x^{2} +17x+60=30x+60[/tex]
- subtracting both sides by 60:
[tex]x^{2} +17x=30x[/tex]
- subtracting both sides by 17x:
[tex]x^{2}=13x[/tex]
- taking 13x to the other side:
[tex]x^{2} -13x=0\\x*(x-13)=0[/tex]
therefore, solution for x : 0 or 13.
