Question 116813
Solve each of the following equations for{{{ x}}}: 



1.


{{{5/(x+6) + 2/(x^2 + 7x + 6) = 3/(x+1)}}}………. replace {{{7x }}} with {{{x+6x}}} 


{{{5/(x+6) + 2/(x^2 + x + 6x + 6) = 3/(x+1)}}}………. group the first two terms together and the last two terms together

{{{5/(x+6) + 2/((x^2 + x )+ (6x + 6)) = 3/(x+1)}}}………. factor a {{{x}}} out of the first group and factor a {{{6}}} out of the second group

{{{5/(x+6) + 2/(x(x + 1 )+ 6(x + 1)) = 3/(x+1)}}}………. combine like terms

{{{5/(x+6) + 2/((x + 6)(x + 1)) = 3/(x+1)}}}……….common denominator is {{{ (x + 6)(x + 1)}}}; multiply both sides by it

{{{(5/(x+6)) (x + 6)(x + 1) + (2/((x + 6)(x + 1))) (x + 6)(x + 1) = (3/(x+1)) (x + 6)(x + 1)}}}……….cancel out

{{{5(x + 1) + 2= 3 (x + 6)}}}……….

{{{5x + 5 + 2= 3 x + 18}}}……….

{{{5x -3x= 18 – 5 - 2}}}……….
{{{2x= 11}}}……….


{{{x= 11/2}}}……….

{{{x= 5.5}}}……….


check:

{{{5/(x+6) + 2/(x^2 + 7x + 6) = 3/(x+1)}}}………. 

{{{5/(5.5+6) + 2/((5.5)^2 + 7*5.5 + 6) = 3/(5.5+1)}}}………. 

{{{5/11.5 + 2/(30.25 + 38.5 + 6) = 3/6.5}}}………. 

{{{0.43 + 2/74.75 = 0.46}}}………. 

{{{0.43 + 0.02675= 0.46}}}………. 

{{{0.456 = 0.46}}}………. 

{{{0.46 = 0.46}}}………. 





2.
{{{2/5 = (x-2)/20}}}………. multiply both sides by {{{20}}}

{{{20*2/5 = 20(x-2)/20}}}………. 


{{{4*2 = (x-2)}}}………. 

{{{8 +2=x }}}

{{{x = 10  }}}

check
{{{2/5 = (x-2)/20}}}………. 

{{{2/5 = (10-2)/20}}}………. 

{{{2/5 = 8/20}}}………. reduce {{{8/20=(8:4)/(20:4)}}}

{{{2 / 5 = 2/ 5}}}………….