Solve the equation. (7)/(3x+6)+(1)/(3)=(5)/(x+2)

Find Common Denominator: First, we need to find a common denominator for the fractions on the left side of the equation to combine them. The common denominator for (3x+6) and 3 is 3(3x+6).Eliminate Denominators: Now, we multiply each fraction by the common denominator to eliminate the denominators. This gives us: (7)(3) + (1)(3x+6) = (5)(3)(3x+6)/(x+2)Distribute Numerators: Next, we distribute the numerators across the terms inside the parentheses: 21 + 3x + 6 = 15(3x+6)/(x+2)Combine Like Terms: Combine like terms on the left side of the equation: 3x + 27 = 15(3x+6)/(x+2)Get Rid of Fraction: Now, we need to get rid of the fraction on the right side of the equation by multiplying both sides by (x+2): (3x + 27)(x+2) = 15(3x+6)Distribute and Combine: Distribute (x+2) on the left side and 15 on the right side: 3x^2 + 6x + 54x + 108 = 45x + 90Set Equation to Zero: Combine like terms on the left side: 3x^2 + 60x + 108 = 45x + 90Factor Quadratic Equation: Subtract 45x and 90 from both sides to set the equation to zero: 3x^2 + 15x + 18 = 0Now, we need to factor the quadratic equation: (3x + 3)(x + 6) = 0

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Solve the equation.
(7)/(3x+6)+(1)/(3)=(5)/(x+2)

Solve the equation. $\newline$ $\frac{7}{3 x+6}+\frac{1}{3}=\frac{5}{x+2}$

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Grade 8

Add and subtract three or more integers

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Q. Solve the equation.

\newline

\frac{7}{3 x+6}+\frac{1}{3}=\frac{5}{x+2}

Find Common Denominator: First, we need to find a common denominator for the fractions on the left side of the equation to combine them. The common denominator for $(3x+6)$ and $3$ is $3(3x+6)$ .
Eliminate Denominators: Now, we multiply each fraction by the common denominator to eliminate the denominators. This gives us: $\newline$ $(7)(3) + (1)(3x+6) = (5)(3)(3x+6)/(x+2)$
Distribute Numerators: Next, we distribute the numerators across the terms inside the parentheses: $21 + 3x + 6 = 15(3x+6)/(x+2)$
Combine Like Terms: Combine like terms on the left side of the equation: $3x + 27 = \frac{15(3x+6)}{x+2}$
Get Rid of Fraction: Now, we need to get rid of the fraction on the right side of the equation by multiplying both sides by $(x+2)$ : $\newline$ $(3x + 27)(x+2) = 15(3x+6)$
Distribute and Combine: Distribute $(x+2)$ on the left side and $15$ on the right side: $\newline$ $3x^2 + 6x + 54x + 108 = 45x + 90$
Set Equation to Zero: Combine like terms on the left side: $3x^2 + 60x + 108 = 45x + 90$
Factor Quadratic Equation: Subtract $45x$ and $90$ from both sides to set the equation to zero: $\newline$ $3x^2 + 15x + 18 = 0$
Factor Quadratic Equation: Subtract $45x$ and $90$ from both sides to set the equation to zero: $\newline$ $3x^2 + 15x + 18 = 0$ Now, we need to factor the quadratic equation: $\newline$ $(3x + 3)(x + 6) = 0$