lim_(x rarr5)(12 x-60)/(x^(2)-6x+5)=

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Substitute x = 5: First, let's try to directly substitute the value of x = 5 into the expression to see if it results in an indeterminate form. (12 * 5 - 60) / (5^2 - 6 * 5 + 5)Calculate Numerator and Denominator: Calculate the numerator and the denominator separately. Numerator: 12 * 5 - 60 = 60 - 60 = 0 Denominator: 5^2 - 6 * 5 + 5 = 25 - 30 + 5 = 0Identify Indeterminate Form: Since both the numerator and the denominator equal 0, we have an indeterminate form of 0/0. We need to simplify the expression further to find the limit.Factor Denominator: Factor the quadratic expression in the denominator. x^2 - 6x + 5 can be factored into (x - 5)(x - 1).Rewrite Limit Expression: Now, rewrite the limit expression with the factored denominator. lim_(x rarr5)(12x - 60) / ((x - 5)(x - 1))Factor Numerator: Notice that the numerator (12x - 60) can be factored as well. Factor out the common term 12. 12(x - 5) / ((x - 5)(x - 1))Cancel Common Term: Now, we can cancel out the common (x - 5) term from the numerator and the denominator. lim_(x rarr5) 12 / (x - 1)Find Limit: Finally, substitute x = 5 into the simplified expression to find the limit. 12 / (5 - 1) = 12 / 4 = 3

$\lim _{x \rightarrow 5} \frac{12 x-60}{x^{2}-6 x+5}=$

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lim⁡x→512x−60x2−6x+5= \lim _{x \rightarrow 5} \frac{12 x-60}{x^{2}-6 x+5}= limx→5​x2−6x+512x−60​=

$\lim _{x \rightarrow 5} \frac{12 x-60}{x^{2}-6 x+5}=$