add and simplify 2v/v^2-64+v/v-8
v/(v^2) = 1/v
v/v = 1
That should give you a start.
9¡Ý1/2v+2
To add and simplify the given expression \( \frac{2v}{v^2-64} + \frac{v}{v-8} \), we need to find a common denominator and then combine the fractions.
Step 1: Factorize the denominators
The denominator \( v^2 - 64 \) is a difference of squares and can be factored as \( (v-8)(v+8) \).
Step 2: Find the least common denominator (LCD)
The least common denominator (LCD) will be the product of all unique factors present in all denominators. In this case, the LCD is \( (v-8)(v+8) \cdot (v-8) \).
Step 3: Rewrite the fractions with the LCD
\( \frac{2v}{v^2-64} + \frac{v}{v-8} = \frac{2v}{(v-8)(v+8)} + \frac{v(v+8)}{(v-8)(v+8)} \).
Step 4: Combine the fractions
Now that the denominators are the same, we can add the numerators.
\( \frac{2v + v(v+8)}{(v-8)(v+8)} \).
Step 5: Simplify the expression
To simplify further, we will expand the numerator and combine like terms.
\( \frac{2v + v^2 + 8v}{(v-8)(v+8)} = \frac{v^2 + 10v}{(v-8)(v+8)} \).
Thus, the simplified form of the expression \( \frac{2v}{v^2-64} + \frac{v}{v-8} \) is \( \frac{v^2 + 10v}{(v-8)(v+8)} \).