Question 69677


You are given:

{{{x/(5x+10) + (x-3)/(x+2) = 7/5}}}

Notice that 5x + 10 can be factored by removing a 5 to make it 5(x+2).  If you do this the equation becomes:

{{{x/5(x+2) + (x-3)/(x+2) = 7/5}}}

Next you need to make all the denominators the same.  The common denominator is 5(x+2) so you don't need to do anything to the first term.  It already has the common denominator.  The second term {{{(x-3)/(x+2)}}} lacks a 5 in the denominator.  Therefore, multiply this term by {{{5/5}}}.  This is equivalent to multiplying the second term by 1 because {{{5/5}}} is 1.  When you do this the equation becomes:

{{{x/5(x+2) + 5(x-3)/5(x+2) = 7/5}}}

Finally, on the right side of the equation the denominator lacks the {{{x+2}}}. Therefore, multiply the right side by {{{(x+2)/(x+2)}}} [effectively multiplying it by 1.  When you do that the equation becomes:

{{{x/5(x+2) + 5(x-3)/5(x+2) = 7(x+2)/5(x+2)}}}

Now you can get rid of the common denominator entirely by multiplying all the terms in the equation by {{{5(x+2)}}}.  This cancels out the denominator and leaves you with the equation:

{{{ x + 5(x-3) = 7(x+2)}}}

Its all downhill from here.  Just do the distributive multiplication on both sides to get:

{{{x + 5x - 15 = 7x+14}}}

Add the two terms containing x on the left side to get:

{{{6x - 15 = 7x + 14}}}

Add 15 to both sides:

{{{6x = 7x + 29}}}

Subtract 7x from both sides:

{{{-x = 29}}}

Multiply both sides by -1:

{{{x = -29}}}

If you substitute this value for x in the original equation, you should find that it makes the left side of the equation equal to{{{7/5}}}

Hope this helps.