Question

Solve for x: 2 over quantity x plus 2 plus 1 over 5 equals 6 over quantity x plus 5.

Answer 1

Answer:

x = 0 and x = 13

Step-by-step explanation:

• given equation :

$\frac{2}{x+2}+\frac{1}{5}=\frac{6}{x+5}$

• solving left part:

$\frac{12+x}{5*(x+2)} =\frac{6}{x+5}$

• multiplying both sides by 5:

$\frac{12+x}{x+2}=\frac{30}{x+5}$

• by cross multiplying:

$x^{2} +17x+60=30x+60$

• subtracting both sides by 60:

$x^{2} +17x=30x$

• subtracting both sides by 17x:

$x^{2}=13x$

• taking 13x to the other side:

$x^{2} -13x=0\\x*(x-13)=0$

therefore, solution for x : 0 or 13.