Question #3db5a

2 Answers
Dec 19, 2017

#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#

Dec 19, 2017

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#