THIS IS REALLY NOT INTERESTING AT ALL BUT I SIMPLY FORGOT HOW TO SOLVE FOR X:
$${\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{\left({\mathtt{X}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}} = {\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{5}}}{\left({\mathtt{X}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}}\right)$$
+130511 Let's multiply through by -1 to get rid of all those nasty negatives !!.....so we have
7/(x+1) = 8 + 5/(x - 2) ....and getting a common denominator on the right , we have....
7/(x+1) = [8(x-2) + 5]/(x-2) ..... simplify on the right
7 /( x+1) = (8x - 16 + 5) / (x-2)
7 / (x+1) = (8x - 11) /(x -2) .....one way to solve this is just to cross-multiply
7(x-2) = (x+1)(8x-11)
7x - 14 = 8x^2 - 3x - 11 ......subtract 7x and add 14 to both sides
0 = 8x^2 - 10x + 3 ......see if this factors
(2x - 1)(4x - 3) = 0
And setting each factor to 0, we have that x = 1/2 or x = 3/4
+130511 Let's multiply through by -1 to get rid of all those nasty negatives !!.....so we have
7/(x+1) = 8 + 5/(x - 2) ....and getting a common denominator on the right , we have....
7/(x+1) = [8(x-2) + 5]/(x-2) ..... simplify on the right
7 /( x+1) = (8x - 16 + 5) / (x-2)
7 / (x+1) = (8x - 11) /(x -2) .....one way to solve this is just to cross-multiply
7(x-2) = (x+1)(8x-11)
7x - 14 = 8x^2 - 3x - 11 ......subtract 7x and add 14 to both sides
0 = 8x^2 - 10x + 3 ......see if this factors
(2x - 1)(4x - 3) = 0
And setting each factor to 0, we have that x = 1/2 or x = 3/4
