Question

Solving a rational equation th Ive for x 3+(4)/(x+6)=-(6)/((x+1)(x+6)) f there is more than one solution, f there is no solution, click on "No

Answer 1

To solve the rational equation 3+(4)/(x+6)=-(6)/((x+1)(x+6)), eliminate the fractions by multiplying by (x+1)(x+6) and then simplify to find the solution for x.

Step-by-step explanation:

To solve the rational equation 3+(4)/(x+6)=-(6)/((x+1)(x+6)), we first eliminate the fractions by multiplying both sides of the equation by (x+1)(x+6) to get rid of the denominators. This gives us (x+1)(x+6)(3+(4)/(x+6))=-(6).

Next, we distribute the (x+1)(x+6) to all terms inside the parentheses, giving us (x+1)(x+6)(3) + (x+1)(x+6)(4)/(x+6) = -(6).

Then, we simplify and solve for x. By canceling out the (x+6) terms, we are left with (x+1)(x+6)(3) + 4 = -(6). Expanding the (x+1)(x+6)(3), we get (x²+7x+6)(3) + 4 = -(6). Finally, we simplify and solve for x to find the solution.