Answer
$\{6\}$.
Work Step by Step
Multiply both sides of the equation by $the LCD (x+5)(x-2)$ to eliminate all fractions.
$(x+5)(x-2)\left (\dfrac{2}{x-2}\right )=(x+5)(x-2) \left (\dfrac{3}{x+5}+\dfrac{10}{(x+5)(x-2)}\right )$
Use the distributive property.on the right side of the equation, and cancel common factors on the left side to obtain:
$2(x+5)=(x+5)(x-2) \left (\dfrac{3}{x+5}\right )+(x+5)(x-2) \left (\dfrac{10}{(x+5)(x-2)}\right )$
Simplify the right side of the equation by cancelling common factors:
$2(x+5)=3(x-2)+10$
Use distributive property.
$2x+10=3x-6+10$
Simplify by combining like terms on each side:
$2x+10=3x+4$
Add $-2x-4$ to both sides.
$2x+10-2x-4=3x+4-2x-4$
Simplify.
$6=x$
Hence, the solution to the equation is $\{6\}$.
