If a/b = 3/7, what is equal to (2a+4b)/(2a-4b)?

To solve the problem, we start with the given ratio ( \frac{a}{b} = \frac{3}{7} ). This means that for every 3 units of ( a ), there are 7 units of ( b ). We can express ( a ) in terms of ( b ):

[

a = \frac{3}{7}b.

]

Next, we substitute this expression for ( a ) into the simplified expression ( \frac{2a + 4b}{2a - 4b} ).

First, calculate ( 2a + 4b ):

[

2a + 4b = 2\left(\frac{3}{7}b\right) + 4b = \frac{6}{7}b + 4b = \frac{6}{7}b + \frac{28}{7}b = \frac{34}{7}b.

]

Next, calculate ( 2a - 4b ):

[

2a - 4b = 2\left(\frac{3}{7}b\right) - 4b = \frac{6}{7}b