Question

number of ways of writing 1/15 in a/3 - b/5 (where a and b are real numbers and a,b are not equal to zero)

Answer 1

Step-by-step explanation:

infinitely many solutions

Answer 2

Answer:

There are infinite ways of writing   $\frac{1}{15}$  in the form  $\frac{a}{3}-\frac{b}{5}$ .

Step-by-step explanation:

Given that   $\frac{a}{3}-\frac{b}{5}$  $=\frac{1}{15}$

Step 1:

Simplifying,

 $\frac{a}{3}-\frac{b}{5}$  $=\frac{1}{15}$

⇒ $\frac{5a-3b}{15}=\frac{1}{15}$

⇒$5a-3b=1$

$\implies 5a=1+3b$

Step 2:

Here, since $5a=1+3b$  we can see that for each value of $a$, we have a corresponding value of $b$. These values can be infinite.

Hence, there are infinite ways of writing   $\frac{1}{15}$  in the form  $\frac{a}{3}-\frac{b}{5}$ .

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