Simplify: ((1)/(4)-(1)/(8x))/((1)/(x)-(1)/(2x^(2))) A) (2x^(2)-x)/(8x-4) B) (2x^(2))/(8x) C) (x)/(4) D) (x)/(6)

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

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Simplify:
((1)/(4)-(1)/(8x))/((1)/(x)-(1)/(2x^(2)))

A) (2x^(2)-x)/(8x-4)

B) (2x^(2))/(8x)

C) (x)/(4)

D) (x)/(6)

Simplify: $\frac{1}{4}-\frac{1}{8x}$ $/$ $\frac{1}{x}-\frac{1}{2x^{2}}$ $\newline$ A) $\frac{2x^{2}-x}{8x-4}$ $\newline$ B) $\frac{2x^{2}}{8x}$ $\newline$ C) $\frac{x}{4}$ $\newline$ D) $\frac{x}{6}$

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Grade 8

Domain and range of functions

Full solution

Q. Simplify:

\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}

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. $\newline$ $(2x^2) / (8x) = x/4$