Question 1143445
<pre>
{{{1/x + 1/(x+1) = 7/12}}}

The LCD is 12x(x+1).  Put that over 1, like this {{{red((12x(x+1))/1)}}}

Multiply every term on both sides by it, like this:

{{{expr(1/x)*red((12x(x+1))/1) + expr(1/(x+1))*red((12x(x+1))/1) = expr(7/12)*red((12x(x+1))/1)}}}

Then cancel like this:

{{{expr(1/cross(x))*red((12cross(x)(x+1))/1) + expr(1/(cross(x+1)))*red((12x(cross(x+1)))/1) = expr(7/cross(12))*(red(cross(12)x(x+1))/1)}}}

and what's left is

{{{red((12(x+1))/1) + red((12x)/1) = expr(7/""^"")*red((x(x+1))/1)}}}

We don't need to write the 1's in the denominators, so we have:

{{{12(x+1)+12x=7x(x+1)}}}

Distribute:

{{{12x+12+12x=7x^2+7x}}}

Combine like terms on the left:

{{{24x+12=7x^2+7x}}}

Swap sides to get the x² term on the left

{{{7x^2+7x=24x+12}}}

Subtract the entire right side from both sides to get 0 on the right

{{{7x^2-17x-12=0}}}

That factors as

{{{(7x+4)(x-3)=0}}}

{{{matrix(3,3,
7x+4=0,";",x-3=0,
7x=-4,";",x=3,
x=-4/7,"","")}}}


Edwin</pre>