(x+7)/x(x-7) -(x-7)/x(x+7)= 7/x2-73

Question

 

 

15y-7=73-y

=15y+y=73+7

=16y=80

=y=80/16

 

Answer 1

Simplify the LHS:

[(x+7)²-(x-7)²]/[x(x²-49)]=(x+7+x-7)(x+7-x+7)/[x(x²-49)]=

(2x)(14)/[x(x²-49)]=28/(x²-49).

So we have:

28/(x²-49)=7/(x²-73),

4/(x²-49)=1/(x²-73),

4(x²-73)=x²-49,

4x²-292=x²-49,

3x²=243,

x²=81, so x=9 or -9.

CHECK

The original equation becomes:

16/18-2/144=7/8,

64/72-1/72=63/72=7/8 which is true so the solution is correct for x=9.

(-2)/((-9)(-16))-(-16)/((-9)(-2))=-2/144+16/18=-1/72+64/72=63/72=7/8, which is true so the solution is correct for x=-9.