Question

HELP PLEASE!!!!

Answer 1

\[\frac{ x+3 }{ x+5 }+\frac{ x }{ 6 }=\frac{ 5 }{ 6 }\]

Answer 2

to add fractions, their denominators must be the same.

when they are not, you must "force it" to be by multiplying it by what is essentially ONE.

\[\frac{ x+3 }{ x+5 } \times \frac{ 6 }{ 6 } + \frac{ x }{ 6 }\times \frac{ x+5 }{ x+5 } = \frac{ 5 }{ 6 }\]
now their denominators are the same and we an add them. [left side]

\[\frac{ 6x + 18 + x^2 + 5x }{ 6x + 30 } = \frac{ 5 }{ 6 }\]

solving for x at this point is done normally.

let me know if you want me to continue solving

Answer 3

I cancel out the 6x right?

Answer 4

Yes can you please continue.

Answer 5

I'll post a solution after you two are done.

Answer 6

Continuing from Euler 271
\[\frac{6x+18+x^2+5x}{6x+30}=\frac{5}{6}\] (cancellin 6 from both sides)
\[\frac{6x+18+x^2+5x}{6(x+5)}=\frac{5}{6}\]
\[\frac{6x+18+x^2+5x}{(x+5)}=\frac{5}{1} \rightarrow 6x+18+x^2+5x =5x+25\]
\[ 6x+18+x^2 =25--(cancelling - 5x- from -both -sides)\]
\[ 6x+18+x^2 -25=0 \rightarrow x^2+6x+18 -25=0\]
\[x^2+6x-7=0 --(writing -standard - form)\]

Answer 7

@christineroxx

Answer 8

\[\frac{x+3}{x+5} + \frac{x}{6} = \frac{5}{6}\]

Subtract x/6 from both sides:

\[\frac{x+3}{x+5} = \frac{5}{6} - \frac{x}{6} \]

Combine fractions on the right side:

\[\frac{x+3}{x+5} = \frac{5 - x}{6} \]

Cross Multiply:

\[6(x+3) = (5 - x)(x + 5)\]

Pull a factor of -1 from (5 - x):
\[6(x+3) = -(x - 5)(x + 5)\]

Multiply everything out on both sides; Notice difference of squares on the right side:

\[6x + 18 = -(x^2 - 25)\]

Continue Simplifying:
\[6x + 18 = -x^2 + 25\]

Put equation in quadratic form:

\[x^2 + 6x + 18 - 25 = 0\]
\[x^2 + 6x - 7 = 0\]

Factor the quadratic:
\[(x + 7)(x- 1) = 0\]

Finish solving for x

Answer 9

THANK YOU!!!!!!