Question

5/x^2-43/x=18? What is the solution to this problem

Answer 1

Let's solve your equation step-by-step.
5
x
2
−
43
x
=
18
5
x
x
+
−
43
x
=
18
Multiply all terms by xx and cancel:
5
+
−
43
x
=
18
x
x
−
43
x
+
5
=
18
x
2
(Simplify both sides of the equation)
−
43
x
+
5
−
18
x
2
=
18
x
2
−
18
x
2
(Subtract 18x^2 from both sides)
−
18
x
2
−
43
x
+
5
=
0
(
−
9
x
+
1
)
(
2
x
+
5
)
=
0
(Factor left side of equation)
−
9
x
+
1
=
0
or
2
x
+
5
=
0
(Set factors equal to 0)
x
=
1
9
or
x
=
−
5
2
Check answers. (Plug them in to make sure they work.)
x
=
1
9
(Works in original equation)
x
=
−
5
2
(Works in original equation)
Answer:
x
=
1
9
or
x
=
−
5
2