Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 28, 2024

Solve the rational equation $\frac{x-2}{2x} + 1 = \frac{x+1}{x}$ . Find the value(s) of $x$ that make the denominator(s) zero, which are the $\varnothing$ restrictions on the variable.

STEP 1

Question: What value of $x$ is not allowed because it makes the denominator zero in the equation $\frac{x-2}{2x} + 1 = \frac{x+1}{x}$ ?
A) $x = 1$ B) $x = 2$ C) $x = -1$ D) $x = 0$
Answer: D

STEP 2

Question: What is the least common denominator (LCD) for the fractions $\frac{x-2}{2x}$ and $\frac{x+1}{x}$ ?
A) $x$ B) $2$ C) $2x$ D) $x^2$
Answer: C

STEP 3

Question: After multiplying each term by the least common denominator 2x, which equation do we get?
A) $(x-2) + 2x = (x+1)$ B) $(x-2) + 2 = 2(x+1)$ C) $(x-2) + 2x = 2(x+1)$ D) $(x-2) + 2(x+1) = x$
Answer: C

STEP 4

Question: What is the simplified form of the equation after distributing and combining like terms?
A) $3x - 2 = 2x + 2$ B) $x - 2 = x + 1$ C) $3x = 2x + 4$ D) $x - 2 = 2x + 2$
Answer: A

STEP 5

Question: What is the value of $x$ after isolating the variable on one side of the equation?
A) $x = 0$ B) $x = 2$ C) $x = 4$ D) $x = -2$
Answer: C

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