Solve (x^2 + x)/x = 8 and Find 2√x | Rational Equation Solution

Published on October 21, 2026

Algebra

Simplify the rational expression (x^2 + x)/x by factoring out x to get x + 1, then solve x + 1 = 8 to find x = 7, so 2√x = 2√7 ≈ 5.29.

Question

Answer

The equation is

Step 1: Simplify the left side.
For

, factor

from the numerator:

Step 2: Solve for .

Step 3: Compute .

Final answer:

Theorems

• Distributive Law (Factoring Out a Common Factor)

For any numbers

, and

. Used here as

• Cancellation of a Nonzero Common Factor

, then

This applies here with

, so

• Subtraction Property of Equality

, then

for any number

. Used to solve

by subtracting

from both sides to get

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