solve 1/ x-3 + 1/x+3 =1/x^2-9
Answers
Answer:
x=1/2
Step-by-step explanation:
1/(x-3)+1/(x+3)=1/(x^2-9)
((x+3)+(x-3))/((x-3)(x+3))=1/(x^2-9)
(x+3+x-3)/(x^2-9)=1/(x^2-9)
2x/(x^2-9)=1/(x^2-9)
2x=1
x=1/2
Answer:
The only configuration that yields a logical answer is:
1
x
+
3
+
1
x
−
3
=
1
x
2
−
9
In which case
x
=
1
2
Explanation:
Considering different configuration:
Configuration 1
Suppose the Left hand side was meant to be
1
x
+
3
+
1
x
−
3
Then the left would be:
(
x
+
3
)
+
(
x
−
3
)
x
2
−
9
Comparing left to right gives
x
+
3
+
x
−
3
=
1
2
x
=
1
x
=
1
2
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Configuration 2
Suppose the Left hand side was meant to be
1
x
+
3
−
1
x
−
3
Then the left would be:
(
x
+
3
)
−
(
x
−
3
)
x
2
−
9
=
6
x
2
−
9
Comparing Left to right would mean that it would have to be true for
6
=
1
Clearly this is a contradiction so it is not the case
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The only possible scenario is for configuration 1