Question

table of contents > module 7: rational expressions and equations > practice: solve rational equati practice: solve rational equations practice: solve rational equations score: 0/6 answered: 0/6 question 1 solve the equation \\(\frac{3}{a} = \frac{2}{a - 5}\\) where a is not equal to 0 or 5 no solution 15 5

Explanation:

Step1: Cross - multiply the equation

To solve the rational equation \(\frac{3}{a}=\frac{2}{a - 5}\), we can cross - multiply. Cross - multiplying gives us \(3\times(a - 5)=2\times a\).

Step2: Expand the left - hand side

Expanding the left - hand side of the equation \(3(a - 5)=2a\), we use the distributive property \(3\times a-3\times5 = 2a\), which simplifies to \(3a-15 = 2a\).

Step3: Solve for \(a\)

Subtract \(2a\) from both sides of the equation \(3a-15 = 2a\). We get \(3a-2a-15=2a - 2a\), which simplifies to \(a-15 = 0\). Then add 15 to both sides: \(a-15 + 15=0 + 15\), so \(a = 15\). We also note that \(a = 15\) does not make the denominators \(a\) or \(a - 5\) equal to zero (since \(15
eq0\) and \(15-5 = 10
eq0\)), so it is a valid solution.

Answer:

15