Solve x: (x+a)+1/(x+a)=c+1/c
Answers
1 Simplify brackets.
\frac{x+a+1}{x+a}+\frac{1}{x+a}=\frac{c+1}{c}
x+a
x+a+1
+
x+a
1
=
c
c+1
2 Simplify \frac{c+1}{c}
c
c+1
to 1+\frac{1}{c}1+
c
1
.
\frac{x+a+1}{x+a}+\frac{1}{x+a}=1+\frac{1}{c}
x+a
x+a+1
+
x+a
1
=1+
c
1
3 Join the denominators.
\frac{x+a+1+1}{x+a}=1+\frac{1}{c}
x+a
x+a+1+1
=1+
c
1
4 Simplify x+a+1+1x+a+1+1 to x+a+2x+a+2.
\frac{x+a+2}{x+a}=1+\frac{1}{c}
x+a
x+a+2
=1+
c
1
5 Multiply both sides by x+ax+a.
x+a+2=(1+\frac{1}{c})(x+a)x+a+2=(1+
c
1
)(x+a)
6 Expand.
x+a+2=x+a+\frac{x}{c}+\frac{a}{c}x+a+2=x+a+
c
x
+
c
a
7 Cancel xx on both sides.
a+2=a+\frac{x}{c}+\frac{a}{c}a+2=a+
c
x
+
c
a
8 Cancel aa on both sides.
2=\frac{x}{c}+\frac{a}{c}2=
c
x
+
c
a
9 Join the denominators.
2=\frac{x+a}{c}2=
c
x+a
10 Multiply both sides by cc.
2c=x+a2c=x+a
11 Subtract aa from both sides.
2c-a=x2c−a=x
12 Switch sides.
x=2c-ax=2c−a