Question 819710
I'm assuming that the expressions are:
{{{1/(p-4)}}} and {{{2/(4-p)}}}
Please put parentheses around numerators and denominators if they are not just a positive integer or variable. So if I am right about your expression then you should have posted:
"... one over (p minus four) and two over (four minus p)"<br>
The answer to this question is tricky. I can show you three different answers, all of which (as far as I know) could be called the lowest common denominator.<br>
Lowest common denominator (LCD):<ul><li>The greatest common factor between the two denominators is 1. When this is true the LCD is the product of the two denominators: (p-4)(4-p). Multiplying we get the LCD:
{{{-p^2+8p-16}}}</li><li>If we recognize that the two denominators are exact opposites of each other then we can come up with simpler LCD's by multiplying the numerator and denominator of <i>one</i> of the fractions by -1/-1:<ul><li>{{{(1/(p-4))((-1)/(-1))}}}
{{{(-1)/(-p+4)}}}
Reordering the denominator:
{{{(-1)/(4+(-p))}}}
Rewriting as a subtraction:
{{{(-1)/(4-p)}}}
This makes (4-p) the LCD.</li><li>{{{(2/(4-p))((-1)/(-1))}}}
{{{(-2)/(-4+p)}}}
Reordering the denominator:
{{{(-2)/(p+(-4))}}}
Rewriting as a subtraction:
{{{(-2)/(p-4))}}}
This makes (p-4) the LCD.</li></ul></li></ul>Personally I prefer the last one: (p-4) because it is simpler and because the variable has a positive coefficient.