Answer: [tex]a=\frac{b(zd-c)}{d}[/tex]
Step-by-step explanation:
Having the following equation given in the exercise:
[tex]z=\frac{a}{b}+\frac{c}{d}[/tex]
You can solve for "a" following this procedure:
1. You can apply the Subtraction property of equality and subtract [tex]\frac{c}{d}[/tex] from both sides of the equation:
[tex]z-(\frac{c}{d})=\frac{a}{b}+\frac{c}{d}-(\frac{c}{d})\\\\z-\frac{c}{d}=\frac{a}{b}[/tex]
2. Now you must subtract the terms on the left side of the equation. Notice that the Least Common Denominator is "d". Then:
[tex]\frac{zd-c}{d}=\frac{a}{b}[/tex]
3. Finally, you can apply the Multiplication property of equality and multiply both sides of the equation by "b". So, you get:
[tex](b)(\frac{zd-c}{d})=(\frac{a}{b})(b)\\\\a=\frac{b(zd-c)}{d}[/tex]
