Question

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

Answer 1

Answer:C

Explanation:

x = 13

Answer 2

`\displaystyle\\ (2)/(x+2) + (1)/(5) = (6)/(x+5)\\\\ (6)/(x+5)-(2)/(x+2) =(1)/(5)\\\\ (6(x+2))/((x+5)(x+2))-(2(x+5))/((x+5)(x+2)) =(1)/(5)\\\\ (6(x+2)-2(x+5))/((x+5)(x+2))=(1)/(5)\\\\ (6x+12-2x-10)/(x^2+2x+5x+10)=(1)/(5)\\\\ (4x+2)/(x^2+7x+10)=(1)/(5)\\\\ x^2+7x+10 = 5(4x+2)\\\\ x^2+7x+10 = 20x+10~~~\Big| -10 \\\\ x^2+7x = 20x \\ \\ x^2 +7x-20x =0\\\\ x^2 - 13x = 0\\\\ x(x-13)=0\\\\ \boxed{x_1 =0}\\\\ x-13=0\\\\ \boxed{x_2=13}`