Solve each equation. Check for extraneous solutions. Homework Help ✎
= x + 1
Square both sides of the equation to remove the radical.
x + 7 = x2 + 2x + 1
Set the equation equal to 0 because it is quadratic (there is an x2-term.)
0 = x2 + x − 6
Factor the polynomial.
Use the Zero Product Property to solve.
Check your solutions in the original equation. Do they both work?
Notice that you can factor x2 + 3x to x(x + 3).
Multiply both sides of the equation by a common denominator to remove the fractions.
2x − (x + 3) = −6
Solve for x.
x = −3
Substitute your solution back into the original equation. Is x = −3 a valid solution to this problem?