1. 12а^3х–16а^2х^2 4а^2х(3а–4х)
а) ------------------------ = ------------------- =
20ах^3–15а^2х^2 5ах^2(4х–3а)
-4а^2х(4х–3а) 4а
= --------------------- = – ----
5ах^2(4х–3а) 5х
х^2–6х+9 (х–3)^2 х–3
б) --------------- = ------------ = -------
9х^2–27х 9х(х–3) 9х
2. 2 5 18+25 43
а) ---- + ----- = --------- = ------
5х 9х 45х 45х
1 1 х+4–х+4 8
б) ----- – ----- = -------------- = -----------
х-4 х+4 (х-4)(х+4) х^2–16
5b 13a^2•5b 5b
в) 13а^2 • --------- = -------------- = -----
26a^3 26a^3 2a
15х^2у 18у 15х^2у•35а^2b
г) ---------- : ---------- = --------------------- =
7а^3 35а^2b 7а^3•18y
5x^2•5b 25x^2b
= ------------ = -----------
6a 6a
3. 6–x^2 6+x x+x^2+6-x^2
a) (x+ ---------) : --------- = ------------------ :
1+x x^2–1 1+x
6+x (x+6)(x-1)(x+1)
: ------------ = ------------------ = x-1
(x-1)(x+1) (1+x)(6+x)
1 4х 1 1
б) ---- + -------- • (----- – -------) =
х-2 4-х^2 х-1 х(х-1)
1 4х х-1
= – ----- + -------------- • -------- =
2-х (2-х)(2+х) х(х-1)
1 4х 4 1
= – ----- + --------------- = ------------- - -----
2-х (2-х)(2+х)х (2-х)(2+х) 2-х
4–2–х 2-х 1
= -------------- = ----------- = ------
(2-х)(2+х) (2-х)(2+х) 2+х