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diate Algerbra 4t #2 corrections:
#12: Solve the equa

(7)/(3x+6)+(1)/(3)=(5)/(x+2)

diate Algerbra $4$ t \# $2$ corrections: $\newline$ \# $12$ : Solve the equa $\newline$ $\frac{7}{3 x+6}+\frac{1}{3}=\frac{5}{x+2}$

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Add and subtract three or more integers

Full solution

Q. diate Algerbra

4

t \#

2

corrections:

\newline

\#

12

: Solve the equa

\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: $\newline$ $(3x + 3)(x + 6) = 0$

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