[tex]\text{We have proportion:}\\\\\dfrac{x}{x-2}=\dfrac{x+5}{x+1}\qquad\text{cross multiply}\\\\x(x+1)=(x-2)(x+5)\qquad\text{use distributive property and FOIL method}\\\\(x)(x)+(x)(1)=(x)(x)+(x)(5)+(-2)(x)+(-2)(5)\\\\x^2+x=x^2+5x-2x-10\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\x=3x-10\qquad\text{subtract 3x from both sides}\\\\-2x=-10\qquad\text{divide both sides by (-2)}\\\\x=5\\\\Answer:\ \boxed{A.\ 5}[/tex]
