5a2-3ab/a2-0,36b2

To simplify the expression \(\frac{5a^2 - 3ab}{a^2 - 0.36b^2}\), we can follow these steps: 1. **Recognize that \(0.36\) can be expressed as \((0.6)^2\):** \[ 0.36b^2 = (0.6b)^2 \] Thus, the denominator can be rewritten: \[ a^2 - 0.36b^2 = a^2 - (0.6b)^2 \] 2. **Identify the denominator as a difference of squares:** \[ a^2 - (0.6b)^2 = (a - 0.6b)(a + 0.6b) \] 3. **Now, factor the numerator \(5a^2 - 3ab\):** We can look for common factors: \[ 5a^2 - 3ab = a(5a - 3b) \] 4. **Now, rewrite the original expression:** \[ \frac{5a^2 - 3ab}{a^2 - 0.36b^2} = \frac{a(5a - 3b)}{(a - 0.6b)(a + 0.6b)} \] So, the simplified expression is: \[ \frac{a(5a - 3b)}{(a - 0.6b)(a + 0.6b)} \] This is the simplified form of the given expression.