Question

rational equations are equations that involve fractions. to solve these equations, first find the least common denominator (lcd) for all the fractions in the equation. next, multiply every term by the least common denominator. then, simplify and solve the resulting equation. finally, verify the solutions bus substituting the \\(x\\)-values into the original equation.

solve the equation \\(\frac{x}{x + 1} + \frac{5}{x - 1} = 1\\).

use the keypad to enter your answer in the box.

the solution of the equation is \\(x = \box\\)

Explanation:

Identify the LCD and domain restrictions

$$
LATEXBLOCK0
$$

Multiply by the LCD and simplify

$$
LATEXBLOCK1
$$

Solve for x and verify

$$
LATEXBLOCK2
$$

Since \(-\frac{3}{2}
e \pm 1\), the solution is valid.

Answer:

The solution of the equation is \(x =\) <blank>\(-\frac{3}{2}\)</blank>