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Solve (5)/(d+6)-(2)/(d-3)=0

Solve 5d+6−2d−3=0 \frac{5}{d+6}-\frac{2}{d-3}=0

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Solve equations with the distributive propertyright chevron icon

Full solution

Q. Solve 5d+6−2d−3=0 \frac{5}{d+6}-\frac{2}{d-3}=0
  1. Combine Fractions: Combine the fractions on the left side of the equation over a common denominator.\newlineTo find a common denominator, multiply the denominators (d+6)(d+6) and (d−3)(d-3) with each other.\newlineCommon denominator = (d+6)(d−3)(d+6)(d-3)\newlineRewrite the equation with the common denominator.\newline(5)(d−3)(d+6)(d−3)−(2)(d+6)(d+6)(d−3)=0\frac{(5)(d-3)}{(d+6)(d-3)} - \frac{(2)(d+6)}{(d+6)(d-3)} = 0
  2. Find Common Denominator: Distribute the numerators over their respective brackets.\newlineMultiply 55 with (d−3)(d-3) and 22 with (d+6)(d+6).\newline5(d−3)−2(d+6)=05(d-3) - 2(d+6) = 0\newline5d−15−2d−12=05d - 15 - 2d - 12 = 0
  3. Distribute Numerators: Combine like terms on the left side of the equation.\newlineCombine the dd terms and the constant terms.\newline(5d−2d)−(15+12)=0(5d - 2d) - (15 + 12) = 0\newline3d−27=03d - 27 = 0
  4. Combine Like Terms: Isolate the variable dd. To isolate dd, add 2727 to both sides of the equation. 3d−27+27=0+273d - 27 + 27 = 0 + 27 3d=273d = 27
  5. Isolate Variable: Solve for dd.\newlineDivide both sides by 33 to find the value of dd.\newline3d3=273\frac{3d}{3} = \frac{27}{3}\newlined=9d = 9

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