14a^3b^5 2b^4
1) -------------- = ----------
21a^4b 3a
x^2 x^2 x
2) ------------ = -------- = --------
x^2+x x(x+1) x+1
a+2b a+2b 1
3) --------------- = ----------------- = --------
a^2 -4b^2 (a+2b)(a-2b) a-2b
1) 2x 2x 2x(x+a) – 2x(x-a)
-------- – ------- = -------------------------- =
x-a x+a (x-a)(x+a)
2x(x+a-x+a) 4ax
= ------------------ = ------------
(x-a)(x+a) (x-a)(x+a)
2) 2-ab 2b 2-ab+2ab
---------- + -------- = ---------------- =
2a+ab 2+b a(2+b)
2-ab
= ---------
a(2+b)
c^2 c^2+c-c^2 c
3) c – ------- = ---------------- = -------
c+1 c+1 c+1
( a a+b ) a–b
3. ------- – ------- • ------- =
( a–b a ) 2b
(a^2– a^2–b^2) • (a–b) b
= ----------------------------------- = – ------
a (a–b) • 2b 2a
4xy 4xy
4. (x + y – ------- ) • ( y – x + ------- ) =
x + y y – x
(x+y)^2 – 4xy (y-x)^2 + 4xy
= -------------------- • ------------------- =
x + y y – x
(x^2 + 2xy + y^2 – 4xy)•(y^2 – 2xy
= --------------------------------------------------
(x + y)(y – x)
+ x^2 + 4xy) (x^2 – 2xy + y^2)•(y^2
----------------- = – ------------------------------
(x + y)(x – y)
+ 2xy + x^2) (x – y)^2 • (y + x)^2
----------------- = – --------------------------- =
(x + y)(x – y)
= – (x – y)(x + y) = y^2 – x^2