Question

Question #3db5a

Answer 1

`x=-3/2`

Explanation:

First, look at the fractions to see if anything can be simplified. Looking at `2/(2x+6)`, you might notice that you can take 2 out the bottom, and that will cancel out the 2 on the top, like this:
`2/(2(x+3))`
`cancel(2)/(cancel(2)(x+3))`
`1/(x+3)`

Then, you can add the two fractions together, like this:
`5/(x+3)+1/(x+3)=6/(x+3)`
Leading to the equation:
`6/(x+3)=4`

Then, you multiply `(x+3)` across the entire equation.
`cancel(x+3)/1*6/cancel(x+3)=4(x+3)`

Then, multiply 4 across the quantity `(x+3)`, leading to the equation:
`6=4x+12`

Then, subtract 12 from both sides, leading to:
`-6=4x`

Then, just divide both sides by 4, and you've managed to get x by itself, so you just have to simplify to have your answer.
`-6/4=x`
`-3/2=x`

Answer 2

Please see the process steps below;

Explanation:

`5/(x + 3) + 2/(2x + 6) = 6`

Take the LCM of the LHS..

`(5(2x + 6) + 2(2x + 3))/((x + 3)(2x + 6)) = 4`

`(10x + 30 +4x + 6)/((x + 3)(2x + 6)) = 4`

Collect like terms..

`(10x + 4x + 30 + 6)/((x + 3)(2x + 6)) = 4`

`(14x + 36)/((x + 3)(2x + 6)) = 4`

Expanding the brackets..

`(14x + 36)/(2x^2 + 6x + 6x + 18) = 4`

`(14x + 36)/(2x^2 + 12x + 18) = 4`

`(14x + 36)/(2x^2 + 12x + 18) = 4/1`

Cross multiplying..

`(14x + 36) xx 1 = (2x^2 + 12x + 18) xx 4`

Simplifying..

`(14x + 36) = 8x^2 + 48x + 72`

Rearranging the equation..

`8x^2 + 48x + 72 = (14x + 36)`

Collecting like terms..

`8x^2 + 48x - 14x + 72 - 36 = 0`

`8x^2 + 34x + 36 = 0 -> "Quadratic Equation"`

Using `-> x = (-b +- sqrt(b^2 - 4ac))/(2a)`

Where;

`a = 8`

`b = 34`

`c = 36`

`x = (-34 +- sqrt((34)^2 - 4(8)(36)))/(2(8))`

`x = (-34 +- sqrt(1156 - 1152))/16`

`x = (-34 +- sqrt 4)/16`

`x = (-34 +- 2)/16`

`x = (-34 + 2)/16 or (-34 - 2)/16`

`x = -32/16 or -36/16`

`x = -2 or -2.25`