Certainly! Let's solve the equation [tex]\( a = \frac{x + c}{x - b} \)[/tex] to make [tex]\( x \)[/tex] the subject.
Step-by-Step Solution:
1. Start with the given equation:
[tex]\[
a = \frac{x + c}{x - b}
\][/tex]
2. To clear the fraction, multiply both sides of the equation by [tex]\( x - b \)[/tex]:
[tex]\[
a(x - b) = x + c
\][/tex]
3. Distribute [tex]\( a \)[/tex] on the left-hand side:
[tex]\[
ax - ab = x + c
\][/tex]
4. To isolate [tex]\( x \)[/tex], first get all terms involving [tex]\( x \)[/tex] on one side of the equation and constant terms on the other side. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
ax - x = ab + c
\][/tex]
5. Factor [tex]\( x \)[/tex] out of the terms on the left side:
[tex]\[
x(a - 1) = ab + c
\][/tex]
6. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\( a - 1 \)[/tex]:
[tex]\[
x = \frac{ab + c}{a - 1}
\][/tex]
So, the solution for [tex]\( x \)[/tex] in terms of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] is:
[tex]\[
x = \frac{ab + c}{a - 1}
\][/tex]
