688 . Cokparrre Apoób: 1) (9x^2-1)/(3x^2)-4x+1

To simplify the expression $\frac{9x^2 - 1}{3x^2 - 4x + 1}$, we can factor both the numerator and the denominator.<br /><br />The numerator $9x^2 - 1$ is a difference of squares and can be factored as $(3x + 1)(3x - 1)$.<br /><br />The denominator $3x^2 - 4x + 1$ can be factored by finding two numbers whose product is $3 \cdot 1 = 3$ and whose sum is $-4$ and $-1$. Therefore, the denominator can be factored as $(3x - 1)(x - 1)$.<br /><br />Now, we can rewrite the expression as:<br /><br />$$\frac{(3x + 1)(3x - 1)}{(3x - 1)(x - 1)}$$<br /><br />We can cancel out the common factor $(3x - 1)$ in the numerator and denominator:<br /><br />$$\frac{3x + 1}{x - 1}$$<br /><br />So, the simplified form of the given expression is $\frac{3x + 1}{x - 1}$.