what is the removable DISCONTINUITIES of each:
1.) y=\frac{10x}{x+3}
2.) y=\frac{3x-2}{x+1}
3.)y=\frac{4x-1}{\left(x+3\right)\left(x-5\right)}
4.)y=\frac{\left(x+4\right)}{\left(x-3\right)\left(x+3\right)}
To identify the removable discontinuities of each function, we need to determine the values of x that make the denominator zero.
1.) For y = (10x)/(x + 3), the denominator (x + 3) is equal to zero when x = -3. Therefore, x = -3 is a removable discontinuity of this function.
2.) For y = (3x - 2)/(x + 1), the denominator (x + 1) is equal to zero when x = -1. Therefore, x = -1 is a removable discontinuity of this function.
3.) For y = (4x - 1)/((x + 3)(x - 5)), both (x + 3) and (x - 5) can make the denominator zero. Setting (x + 3) = 0, we find x = -3. Setting (x - 5) = 0, we find x = 5. Therefore, x = -3 and x = 5 are removable discontinuities of this function.
4.) For y = (x + 4)/((x - 3)(x + 3)), both (x - 3) and (x + 3) can make the denominator zero. Setting (x - 3) = 0, we find x = 3. Setting (x + 3) = 0, we find x = -3. Therefore, x = 3 and x = -3 are removable discontinuities of this function.