If \frac{x + 5}{x - 1} = 3, what is the value of x + 1? — SAT

If $\frac{x + 5}{x - 1} = 3$ , what is the value of $x + 1$ ?

The correct answer is

5

. To solve the rational equation

\frac{x + 5}{x - 1} = 3

, we first multiply both sides of the equation by

x - 1

, which gives

x + 5 = 3(x - 1)

. Distributing the

3

on the right side yields

x + 5 = 3x - 3

. Subtracting

x

from both sides gives

5 = 2x - 3

. Adding

3

to both sides yields

8 = 2x

. Dividing both sides by

2

gives

x = 4

. Substituting this value back into the expression

x + 1

yields

4 + 1 = 5

Multiply both sides of the equation by

x - 1

to clear the fraction.

x + 5 = 3(x - 1)

Multiplying both sides by the denominator clears the fraction and allows us to solve the equation linearly.

Distribute the

3

to the terms inside the parentheses on the right side of the equation.

x + 5 = 3x - 3

This step simplifies the equation to prepare for isolating the variable

x

Isolate the variable

x

by subtracting

x

from both sides and then adding

3

to both sides.

8 = 2x

Grouping like terms on opposite sides of the equation simplifies the process of finding the value of the variable.

Divide both sides of the equation by

2

to find the value of

x

x = 4

Dividing by the coefficient of

x

isolates the variable completely.

Substitute the value of

x

into the expression

x + 1

to find the final answer.

4 + 1 = 5

The question asks for the value of the expression

x + 1

, not just the value of

x

Solving rational equations that simplify to linear equations

Question