Study Paths $\newline$ TX Math Bridge - Stage $2$ Study Path $\newline$ Test $\newline$ Test $\newline$ Unit: Rational Expressions $\newline$ Progress: $\newline$ The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answe $\newline$ Simplify: $\newline$ $\frac{1}{4}-\frac{1}{8x}$ $/$ $\frac{1}{x}-\frac{1}{2x^{2}}$ $\newline$ $\frac{2x^{2}-x}{8x-4}$ $\newline$ $\frac{2x^{2}}{8x}$ $\newline$ $\frac{x}{4}$ $\newline$ $\frac{x}{6}$

Full solution

Q. Study Paths

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TX Math Bridge - Stage

2

Study Path

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Test

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Test

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Unit: Rational Expressions

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Progress:

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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answe

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Simplify:

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\frac{1}{4}-\frac{1}{8x}

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\frac{1}{x}-\frac{1}{2x^{2}}

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\frac{2x^{2}-x}{8x-4}

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\frac{2x^{2}}{8x}

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\frac{x}{4}

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\frac{x}{6}

Simplify numerator: Step $1$ : Simplify the numerator. $\newline$ We start by finding a common denominator for the terms in the numerator: $\newline$ $(\frac{1}{4}) - (\frac{1}{8x}) = (\frac{2x}{8x}) - (\frac{1}{8x}) = (\frac{2x - 1}{8x})$
Simplify denominator: Step $2$ : Simplify the denominator. $\newline$ Next, we find a common denominator for the terms in the denominator: $\newline$ $(\frac{1}{x}) - (\frac{1}{2x^2}) = (\frac{2x}{2x^2}) - (\frac{1}{2x^2}) = (\frac{2x - 1}{2x^2})$
Divide numerator by denominator: Step $3$ : Divide the simplified numerator by the simplified denominator. $\newline$ We use the property $(a/b) / (c/d) = (a\cdot d) / (b\cdot c)$ : $\newline$ $\left(\frac{2x - 1}{8x}\right) / \left(\frac{2x - 1}{2x^2}\right) = \left(\frac{(2x - 1) \cdot (2x^2)}{(8x) \cdot (2x - 1)}\right)$
Simplify expression: Step $4$ : Simplify the expression. $\newline$ Since $(2x - 1)$ appears in both numerator and denominator, it cancels out: $\newline$ $\frac{(2x - 1) \cdot (2x^2)}{(8x) \cdot (2x - 1)} = \frac{2x^2}{8x}$
Further simplify expression: Step $5$ : Further simplify the expression. $\newline$ $(2x^2) / (8x) = x/4$