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

Combine Fractions: Combine the fractions on the left side of the equation over a common denominator. To find a common denominator, multiply the denominators (d+6) and (d-3) with each other. Common denominator = (d+6)(d-3) Rewrite the equation with the common denominator. (5)(d-3)/(d+6)(d-3) - (2)(d+6)/(d+6)(d-3) = 0Find Common Denominator: Distribute the numerators over their respective brackets. Multiply 5 with (d-3) and 2 with (d+6). 5(d-3) - 2(d+6) = 0 5d - 15 - 2d - 12 = 0Distribute Numerators: Combine like terms on the left side of the equation. Combine the d terms and the constant terms. (5d - 2d) - (15 + 12) = 0 3d - 27 = 0Combine Like Terms: Isolate the variable d. To isolate d, add 27 to both sides of the equation. 3d - 27 + 27 = 0 + 27 3d = 27Isolate Variable: Solve for d. Divide both sides by 3 to find the value of d. 3d / 3 = 27 / 3 d = 9

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

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Math Problems

Grade 8

Solve equations with the distributive property

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Q. Solve

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

Combine Fractions: Combine the fractions on the left side of the equation over a common denominator. $\newline$ To find a common denominator, multiply the denominators $(d+6)$ and $(d-3)$ with each other. $\newline$ Common denominator = $(d+6)(d-3)$ $\newline$ Rewrite the equation with the common denominator. $\newline$ $\frac{(5)(d-3)}{(d+6)(d-3)} - \frac{(2)(d+6)}{(d+6)(d-3)} = 0$
Find Common Denominator: Distribute the numerators over their respective brackets. $\newline$ Multiply $5$ with $(d-3)$ and $2$ with $(d+6)$ . $\newline$ $5(d-3) - 2(d+6) = 0$ $\newline$ $5d - 15 - 2d - 12 = 0$
Distribute Numerators: Combine like terms on the left side of the equation. $\newline$ Combine the $d$ terms and the constant terms. $\newline$ $(5d - 2d) - (15 + 12) = 0$ $\newline$ $3d - 27 = 0$
Combine Like Terms: Isolate the variable $d$ . To isolate $d$ , add $27$ to both sides of the equation. $3d - 27 + 27 = 0 + 27$ $3d = 27$
Isolate Variable: Solve for $d$ . $\newline$ Divide both sides by $3$ to find the value of $d$ . $\newline$ $\frac{3d}{3} = \frac{27}{3}$ $\newline$ $d = 9$