Solve for x: (x + 3)/(x - 1) = 5

• A. -2
• B. 2
• C. 3
• D. 1

Answer: (B)

The essential technique is clearing the fraction by multiplying by the denominator, turning the problem into a simple linear equation, while remembering that the denominator cannot be zero.

Starting with (x + 3)/(x − 1) = 5, multiply both sides by (x − 1): x + 3 = 5(x − 1) = 5x − 5.

Bring like terms together: subtract x from both sides to get 3 = 4x − 5, then add 5 to both sides to obtain 8 = 4x, so x = 2.

Check by substitution: (2 + 3)/(2 − 1) = 5/1 = 5, which works. Also note x cannot be 1, but 2 is allowed.

Therefore, x equals 2.