Question 78353
I assume you mean; (a few brackets would help remove all doubt)
:
{{{3/((x-2))}}} + {{{21/((x^2-4))}}} = {{{14/((x+2))}}}
:
Notice that (x^2 - 4) is the difference of squares, can be factored to:
{{{3/((x-2))}}} + {{{21/((x-2)(x+2))}}} = {{{14/((x+2))}}}
:
If we multiply thru by (x-2)(x+2) we have:
:
3(x+2) + 21 = 14(x-2)
:
Multiply what's inside the brackets and do some basic algebra:
3x + 6 + 21 = 14x - 28
3x + 27 = 14x - 28
3x - 14x = -28 - 27
-11x = -55
x = -55/-11
x = +5
:
:
Check our solution of x=5 for equality in the original equation:
{{{3/((5-2))}}} + {{{21/((5^2-4))}}} = {{{14/((5+2))}}}
:
{{{3/((3))}}} + {{{21/((21))}}} = {{{14/((7))}}}; confirms our solution
:
How about this? Did you understand what went on here?