Question

Simplify 2(a-3)/(a-4)(a-5)+(a-1)/(3-a)(a-4)+(a-2)/(5-a)(a-3)​

Answer 1

Answer:

  $\dfrac{5}{x^3-12x^2+47x-60}$

Step-by-step explanation:

Though it is not what you have written, we think you want to simplify ...

  $\dfrac{2(a-3)}{(a-4)(a-5)}+\dfrac{(a-1)}{(3-a)(a-4)}+\dfrac{(a-2)}{(5-a)(a-3)}\\\\=\dfrac{2(a-3)^2}{(a-3)(a-4)(a-5)}+\dfrac{-(a-1)(a-5)}{(a-3)(a-4)(a-5)}+\dfrac{-(a-2)(a-4)}{(a-3)(a-4)(a-5)}\\\\=\dfrac{2(a^2-6a+9)-(a^2-6a+5)-(a^2-6a+8)}{x^3-12x^2+47x-60}\\\\=\boxed{\dfrac{5}{x^3-12x^2+47x-60}}$

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When writing a fraction in plain text, parentheses are needed around the entire denominator. The order of operations tells you that a/bc = (a/b)c, not a/(bc).