<PRE><B>Question 197468</B>
a) Solve for n and check:
{{{((n+6))/3}}} - {{{((n-3))/2}}} = 2
Multiply by 6 to get rid of the denominators
6*{{{((n+6))/3}}} - 6*{{{((n-3))/2}}} = 6(2)
Cancel out the denominators
2(n+6) - 3(n-3) = 12
:
2n + 12 - 3n + 9 = 12
;
-n + 21 = 12
:
-n = 12 - 21
:
-n = -9
Multiply both sides by -1; (n has to be positive)
n = +9
:
Check solution in original equation; substitute 9 for n
{{{((9+6))/3}}} - {{{((9-3))/2}}} = 2
{{{((15))/3}}} - {{{((6))/2}}} = 2
5 - 3 = 2
:
:
b) Perform the indicated operation and express the result in lowest terms:
{{{((x^2-9))/((x-3))}}} * {{{((4x+8))/((x^2+5x+6))}}}
Factor
{{{((x-3)(x+3))/((x-3))}}} * {{{(4(x+2))/((x+3)(x+2))}}} = 4
Look at this, everything cancels leaving just 4</PRE>