5х2+9/6 - 4х2-9/5

To simplify the expression \( 5x^2 + \frac{9}{6} - 4x^2 - \frac{9}{5} \), follow these steps:

1. Combine the like terms \( 5x^2 - 4x^2 \): \[ 5x^2 - 4x^2 = 1x^2 = x^2 \]

2. Simplify the fractions: \[ \frac{9}{6} = \frac{3}{2} \quad (\text{by dividing the numerator and denominator by 3}) \] \[ \frac{9}{5} \text{ is already in simplest form.} \]

3. Now, combine the simplified fractions: \[ \frac{3}{2} - \frac{9}{5} \]

   To combine these fractions, find a common denominator. The least common multiple of 2 and 5 is 10.

   Convert each fraction: \[ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \] \[ \frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10} \]

4. Now, combine the fractions: \[ \frac{15}{10} - \frac{18}{10} = \frac{15 - 18}{10} = \frac{-3}{10} \]

5. Putting it all together, the simplified expression is: \[ x^2 - \frac{3}{10} \]

Thus, the final simplified expression is: \[ x^2 - \frac{3}{10} \]