Question 147259
Hi, Hope I can help,
.
Solve and check each of the following for X: 
A: {{{(x/12)-(1/6)=((2x-7)/12) }}} 
B: {{{ (5/(x+6))+(2/(x^2+7x+6))=(3(x+1)) }}}
.
First we will solve equation A
.
A: {{{(x/12)-(1/6)=((2x-7)/12) }}} 
.
First, you have to get the same denominator for all the fractions, you have to change {{{ 1/6 }}} to {{{ 2/12 }}}
.
Now we can put {{{ 2/12 }}} in place of {{{ 1/6 }}} in the equation
.
A: {{{(x/12)-(2/12)=((2x-7)/12) }}}
.
Now we can subtract on the left side
.
A: {{{(x - 2)/12=((2x-7)/12) }}}  
.
Now we will use cross multiplication to get rid of the fractions
.
{{{ 12(2x-7) = 12 ( x - 2 ) }}}
.
Now we will multiply the both sides
.
{{{ 24x - 84 = 12x - 24 }}}
.
Now we can solve for "x"
{{{ 24x - 12x - 84 = 12x - 12x - 24 }}}
.
{{{ 12x - 84 + 84 = -24 + 84 }}}
.
{{{ 12x = 60 }}}
.
{{{ (12x)/12 = 60/12 }}}
.
{{{ x = 5 }}}
x = "5"
We can check by replacing "x" with "5" in the original equation
 .
A: {{{(x/12)-(1/6)=((2x-7)/12) }}} 
.
A: {{{ (5/12)-(1/6)=(2(5)-7)/12 }}}
.
W have to change {{{ 1/6 }}} to {{{ 2/12 }}} again
.
A: {{{(5/12)-(2/12)=((2(5)-7)/12) }}} 
. 
A: {{{(5-2)/12=(10-7)/12) }}}
. 
A: {{{ 3/12=3/12 }}}
.
The answer to Equation A: is "5"   
.
Now we will solve equation B
.
B: {{{ (5/(x+6))+(2/(x^2+7x+6))=(3(x+1)) }}}
.
You don't have to change the right side, but you need to change {{{ (x+6) }}} to {{{ (x^2+7x+6) }}} 
.
{{{ (x^2+7x+6) }}} has factors of (x+1) and (x+6) (the factors of 6 add up to 7)
.
We need to multiply  {{{ 5/(x+6) }}} by {{{ (x+1)/(x+1) }}} to make the same denominator
.
B: {{{ (5(x+1)/(x^2+7x+6)) +(2/(x^2+7x+6))=(3(x+1)) }}}
.
Now we need to multiply 5(x+1)
.
B: {{{ (5x+5)/(x^2+7x+6)) +(2/(x^2+7x+6))=(3(x+1)) }}}
.
Now we can add the left side
.
B: {{{ ((5x+5)+ 2)/(x^2+7x+6)=(3(x+1)) }}}
.
B: {{{ (5x+7)/(x^2+7x+6)=(3(x+1)) }}}
.
Now we will multiply the right side using the distributive property
.
B: {{{ (5x+7)/(x^2+7x+6)=(3x+3)/1 }}}
.
Now we will use cross multiplication
.
{{{ (5x+7)(1) = (3x+3)(x^2+7x+6) }}}
.
It will end up to be
.
{{{ 5x+7 = 3(x^3) + 24(x^2) + 39x + 18 }}}
.
We will now put everything on one side
.
{{{ 5x -5x +7 - 7 = 3(x^3) + 24(x^2) + 39x - 5x + 18 - 7 }}}
.
{{{ 3(x^3) + 24(x^2) + 34x + 11 = 0 }}}
.
It is a cubic equation, the best way to get the answer is to use a cubic equation calculator on the computer. ( You can't really memorize the cubic equation formula, because it is way to big, and complicated)
.
The three answers to equation "B" are rounded to
.
x(1) =   -0.47075530247265
x(2) =   -6.29117730768554
x(3) =   -1.2380673898418
.
Hope I helped, Levi