If `(a^(2)-bc)/(a^(2) +bc) + (b^(2)-ac)/(b^(2) + ac) + (c^(2)-ab)/(c^(2)+ab)= 1` then find `(a^(2))/(a^(2) + bc) + (b^(2))/(b^(2) + ac) + (c^(2))/(c^(2) +ab)=`?

Answer

To solve the given equation

\[ \frac{a^2 - bc}{a^2 + bc} + \frac{b^2 - ac}{b^2 + ac} + \frac{c^2 - ab}{c^2 + ab} = 1, \]

we need to find the value of

\[ \frac{a^2}{a^2 + bc} + \frac{b^2}{b^2 + ac} + \frac{c^2}{c^2 + ab}. \]

### Step 1: Rewrite the Given Equation

We can rewrite each term in the given equation:

\[ \frac{a^2 - bc}{a^2 + bc} = 1 - \frac{2bc}{a^2 + bc}, \]
\[ \frac{b^2 - ac}{b^2 + ac} = 1 - \frac{2ac}{b^2 + ac}, \]
\[ \frac{c^2 - ab}{c^2 + ab} = 1 - \frac{2ab}{c^2 + ab}. \]

### Step 2: Substitute Back into the Equation

Substituting these into the equation gives:

\[ \left(1 - \frac{2bc}{a^2 + bc}\right) + \left(1 - \frac{2ac}{b^2 + ac}\right) + \left(1 - \frac{2ab}{c^2 + ab}\right) = 1. \]

This simplifies to:

\[ 3 - \left(\frac{2bc}{a^2 + bc} + \frac{2ac}{b^2 + ac} + \frac{2ab}{c^2 + ab}\right) = 1. \]

### Step 3: Isolate the Sum of Fractions

Rearranging gives:

\[ \frac{2bc}{a^2 + bc} + \frac{2ac}{b^2 + ac} + \frac{2ab}{c^2 + ab} = 2. \]

### Step 4: Find the Required Expression

Now, we need to find:

\[ \frac{a^2}{a^2 + bc} + \frac{b^2}{b^2 + ac} + \frac{c^2}{c^2 + ab}. \]

Notice that:

\[ \frac{a^2}{a^2 + bc} = 1 - \frac{bc}{a^2 + bc}, \]
\[ \frac{b^2}{b^2 + ac} = 1 - \frac{ac}{b^2 + ac}, \]
\[ \frac{c^2}{c^2 + ab} = 1 - \frac{ab}{c^2 + ab}. \]

### Step 5: Substitute Back into the Expression

Substituting these into the expression gives:

\[ \left(1 - \frac{bc}{a^2 + bc}\right) + \left(1 - \frac{ac}{b^2 + ac}\right) + \left(1 - \frac{ab}{c^2 + ab}\right). \]

This simplifies to:

\[ 3 - \left(\frac{bc}{a^2 + bc} + \frac{ac}{b^2 + ac} + \frac{ab}{c^2 + ab}\right). \]

### Step 6: Relate to Previous Result

From our previous result, we know that:

\[ \frac{bc}{a^2 + bc} + \frac{ac}{b^2 + ac} + \frac{ab}{c^2 + ab} = 1. \]

### Step 7: Final Calculation

Thus, we have:

\[ \frac{a^2}{a^2 + bc} + \frac{b^2}{b^2 + ac} + \frac{c^2}{c^2 + ab} = 3 - 1 = 2. \]

### Final Answer

The value is

\[ \boxed{2}. \]