Question

Solving a Rational Equation in the Form of a Proportio

Solve and check:
1 x+10
x+3 x-2
From least to greatest, the solutions are x =
DONE ✔
and x =

Answer 1

To solve the rational equation (1(x+10)/(x+3) = (x-2)), cross-multiply and simplify to find the quadratic equation involved. Solve the quadratic equation using the quadratic formula to obtain the solutions. Finally, check the solutions by substituting them back into the original equation.

Step-by-step explanation:

To solve the rational equation 1(x+10)/(x+3) = (x-2), we need to eliminate the denominators by cross-multiplying.

This gives us the equation (x+10)(x-2) = 1(x+3).

Simplifying and solving for x, we have x2 -12x -23 = 0.

Using the quadratic formula, the solutions to the equation are x = 6 + sqrt(59) and x = 6 - sqrt(59).

Let's check these solutions by substituting them back into the original equation. If both sides are equal, then the solutions are valid.

Learn more about Solving Rational Equations