What is the answer of Y²-36/Y²-49•Y+6/Y+7?
Answer (1)
Answer:Y^2 - 36 = (Y - 6)(Y + 6)Step-by-step explanation:To simplify the expression \(\frac{Y^2 - 36}{Y^2 - 49} \cdot \frac{Y + 6}{Y + 7}\), follow these steps:1. **Factorize the expressions in the numerators and denominators:** - \(Y^2 - 36\) is a difference of squares: \[ Y^2 - 36 = (Y - 6)(Y + 6) \] - \(Y^2 - 49\) is also a difference of squares: \[ Y^2 - 49 = (Y - 7)(Y + 7) \]2. **Rewrite the original expression with these factors:** \[ \frac{(Y - 6)(Y + 6)}{(Y - 7)(Y + 7)} \cdot \frac{Y + 6}{Y + 7} \]3. **Combine the fractions:** \[ \frac{(Y - 6)(Y + 6) \cdot (Y + 6)}{(Y - 7)(Y + 7) \cdot (Y + 7)} \]4. **Simplify by canceling common factors:** - The factor \(Y + 6\) in the numerator and denominator cancels out: \[ \frac{(Y - 6) \cdot (Y + 6)}{(Y - 7) \cdot (Y + 7)} \] - The factor \(Y + 7\) in the numerator and denominator cancels out: \[ \frac{Y - 6}{Y - 7} \]Thus, the simplified expression is:\[\frac{Y - 6}{Y - 7}kindly brainly? thank you!
