Answer:
x: {-3, 5}
Step-by-step explanation:
Step 1. Find least common denominator
Step 2. Multiply missing factors on top AND bottom
Step 3. Combine like terms
Step 4. Simplify (get rid of denominator)
Step 5. Solve for x
[tex]\frac{x}{x-5} +\frac{3}{x+2} =\frac{7x}{x^2-3x-10}[/tex] LCD = [tex]x^2-3x-10[/tex] OR [tex](x-5)(x+2)[/tex]
[tex]\frac{x}{x-5}(\frac{x+2}{x+2}) +\frac{3}{x+2}(\frac{x-5}{x-5}) =\frac{7x}{x^2-3x-10}[/tex]
[tex]\frac{x(x+2)}{(x-5)(x+2)} +\frac{3(x-5)}{(x+2)(x-5)} =\frac{7x}{(x-5)(x+2)}[/tex]
[tex]\frac{x(x+2)+3(x-5)}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}[/tex]
[tex]\frac{x^2+2x+3x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}[/tex]
[tex]\frac{x^2+5x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}[/tex]
[tex]x^2+5x-15=7x[/tex]
[tex]x^2-2x-15[/tex]
[tex](x-5)(x+3)[/tex]
x = -3, 5
