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Express ((1)/(3x)+(2)/(y))/((2)/(x)) as a fraction in its simplest form. CHAPTER 6 143

88. Express 13x+2y2x \frac{\frac{1}{3 x}+\frac{2}{y}}{\frac{2}{x}} as a fraction in its simplest form.\newlineCHAPTER 66\newline143143

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Q. 88. Express 13x+2y2x \frac{\frac{1}{3 x}+\frac{2}{y}}{\frac{2}{x}} as a fraction in its simplest form.\newlineCHAPTER 66\newline143143
  1. Combine terms over common denominator: Combine the terms in the numerator over a common denominator, which is 3xy3xy. \newline(13x+2y)=y+6x3xy\left(\frac{1}{3x}+\frac{2}{y}\right) = \frac{y + 6x}{3xy}
  2. Divide combined fraction by 2/x2/x: Now, divide the combined fraction by 2/x2/x. y+6x3xy/2x=y+6x3xy×x2\frac{y + 6x}{3xy} / \frac{2}{x} = \frac{y + 6x}{3xy} \times \frac{x}{2}
  3. Multiply numerators and denominators: Multiply the numerators and the denominators. (y+6x)/(3xy)×x/2=(x(y+6x))/(6xy)(y + 6x)/(3xy) \times x/2 = (x(y + 6x))/(6xy)
  4. Simplify expression by canceling: Simplify the expression by canceling out the common xx in the numerator and denominator.x(y+6x)6xy=y+6x6y\frac{x(y + 6x)}{6xy} = \frac{y + 6x}{6y}
  5. Check for further simplification: Check if the expression can be simplified further. Since there are no common factors between the numerator and the denominator, the expression is in its simplest form.

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