When x=5 and y=2 , the expression
`(xy)/(70)+(9)/(5(x+y))+(1)/(x+y)=?`

Options

A. `(19)/(35)`
B. `(58)/(105)`
C. `(1)/(2)`
D. `(4)/(7)`

Answer

To solve the expression \(\frac{xy}{70} + \frac{9}{5(x+y)} + \frac{1}{x+y}\) when \(x = 5\) and \(y = 2\), we will follow these steps:

### Step 1: Substitute the values of \(x\) and \(y\)
We start by substituting \(x = 5\) and \(y = 2\) into the expression.

\[ \frac{xy}{70} + \frac{9}{5(x+y)} + \frac{1}{x+y} = \frac{(5)(2)}{70} + \frac{9}{5(5+2)} + \frac{1}{5+2} \]

### Step 2: Calculate \(xy\)
Calculate \(xy\):

\[ xy = 5 \times 2 = 10 \]

Now substitute this back into the expression:

\[ \frac{10}{70} + \frac{9}{5(7)} + \frac{1}{7} \]

### Step 3: Simplify \(\frac{10}{70}\)
Simplify \(\frac{10}{70}\):

\[ \frac{10}{70} = \frac{1}{7} \]

So, the expression now looks like:

\[ \frac{1}{7} + \frac{9}{35} + \frac{1}{7} \]

### Step 4: Convert \(\frac{1}{7}\) to a common denominator
To add these fractions, we need a common denominator. The least common multiple of 7 and 35 is 35. Convert \(\frac{1}{7}\) to have a denominator of 35:

\[ \frac{1}{7} = \frac{5}{35} \]

Now substitute this back into the expression:

\[ \frac{5}{35} + \frac{9}{35} + \frac{5}{35} \]

### Step 5: Combine the fractions
Now, combine the fractions:

\[ \frac{5 + 9 + 5}{35} = \frac{19}{35} \]

### Final Answer
Thus, the value of the expression is:

\[ \frac{19}{35} \]