BÀI TẬP RÚT GỌN PHÂN THỨC
TOÁN LỚP 8
Bài 1. Rút gọn các phân thức sau:
a) \(\frac{{{x}^{2}}-16}{4\text{x}-{{x}^{2}}}\,\,(x\ne 0,\,x\ne 4)\)
b) \(\frac{{{x}^{2}}+4x+3}{2\text{x}+6}\,\,(x\ne -3)\)
c) \(\frac{15\text{x}{{(x+y)}^{3}}}{5y{{(x+y)}^{2}}}\,\,(y+(x+y)\ne 0)\)
d) \(\frac{5(x-y)-3(y-x)}{10(x-y)}\,\,(x\ne y)\)
e) \(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}\,\,(x\ne -y)\)
f) \(\frac{{{x}^{2}}-xy}{3\text{x}y-3{{y}^{2}}}\,\,(x\ne y,\,y\ne 0)\)
g) \(\frac{2\text{a}{{\text{x}}^{2}}-4\text{ax}+2\text{a}}{5b-5b{{\text{x}}^{2}}}\,\,(b\ne 0,\,x\ne \pm 1)\)
h) \(\frac{4{{\text{x}}^{2}}-4\text{x}y}{5{{\text{x}}^{3}}-5{{\text{x}}^{2}}y}\,\,(x\ne 0,\,x\ne y)\)
i) \(\frac{{{(x+y)}^{2}}-{{z}^{2}}}{x+y+z}\,\,(x+y+z\ne 0)\)
k) \(\frac{{{x}^{6}}+2{{\text{x}}^{3}}{{y}^{3}}+{{y}^{6}}}{{{x}^{7}}-x{{y}^{6}}}\,\,(x\ne 0,\,x\ne \pm y)\)
Bài 2. Rút gọn các biểu thức.
a) \(\frac{{{m}^{4}}-m}{2{{m}^{2}}+2m+2}\) b) \(\frac{a{{b}^{2}}+{{a}^{3}}-{{a}^{2}}b}{{{a}^{3}}b+{{b}^{4}}}\)
c) \(\frac{xy+1-x-y}{y+z-1-yz}\) d) \(\frac{ax+ay-bx-by}{ax-ay-bx+by}\);
e) \(\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}+2ab}{{{a}^{2}}-{{b}^{2}}+{{c}^{2}}+2ac}\) f) \(\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}-a-b-{{b}^{2}}}\)
g) \(\frac{{{a}^{3}}+1}{2{{a}^{2}}+4a+2}\) h) \(\frac{{{a}^{3}}({{b}^{2}}-{{c}^{2}})+{{b}^{3}}({{c}^{2}}-{{a}^{2}})+{{c}^{3}}({{a}^{2}}-{{b}^{2}})}{{{a}^{2}}(b-c)+{{b}^{2}}(c-a)+{{c}^{2}}(a-b)}\)
i) \(\frac{{{x}^{2}}-(a+b)x+ab}{{{x}^{2}}-(a-b)x-ab}\); j) \(\frac{{{x}^{2}}+{{a}^{2}}-{{b}^{2}}-2bc+2ax-{{c}^{2}}}{{{x}^{2}}+{{b}^{2}}-{{a}^{2}}+2bx-2ac-{{c}^{2}}}\);
k) \(\frac{3{{x}^{3}}-2{{x}^{2}}+4x-5}{6{{x}^{2}}+3x-9}\) l) \(\frac{x\left| x-2 \right|}{{{x}^{2}}-5x+6}\)
n) \(\frac{{{a}^{2x}}-{{b}^{2x}}}{{{a}^{x}}+{{b}^{x}}}\); m) \(\frac{1-{{(2a+3b)}^{2}}}{2a+3b+1}\)
o) \(\frac{{{3}^{3x}}-{{3}^{3y}}}{{{3}^{x}}+{{3}^{y}}}\) ơ) \(\frac{{{2}^{4m}}-{{2}^{4n}}}{{{2}^{2n}}+{{2}^{2m}}}\)
p) \(\frac{{{a}^{2}}(b-c)+{{b}^{2}}(c-a)+{{c}^{2}}(a-b)}{a{{b}^{2}}-a{{c}^{2}}-{{b}^{3}}+b{{c}^{2}}}\) q) \(\frac{2{{x}^{3}}-7{{x}^{2}}-12x+45}{3{{x}^{3}}-19{{x}^{2}}+33x-9}\);
u) \(\frac{{{x}^{3}}-{{y}^{3}}+{{z}^{3}}+3xyz}{{{(x+y)}^{2}}+{{(y+z)}^{2}}+{{(z-x)}^{2}}}\(; ư) \(\frac{{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz}{{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}}\)
Bài 3: Rút gọn, rồi tính giá trị các phân thức sau:
a) \(A=\frac{(2{{\text{x}}^{2}}+2\text{x}){{(x-2)}^{2}}}{({{x}^{3}}-4\text{x})(x+1)}\( với \(x=\frac{1}{2}\)
b) \(B=\frac{{{x}^{3}}-{{x}^{2}}y+x{{y}^{2}}}{{{x}^{3}}+{{y}^{3}}}\( với \(x=-5,\,y=10\)
Bài 4: Rút gọn các phân thức sau:
a) \(\frac{{{(a+b)}^{2}}-{{c}^{2}}}{a+b+c}\(
b) \(\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}+2\text{a}b}{{{a}^{2}}-{{b}^{2}}+{{c}^{2}}+2\text{a}c}\)
c) \(\frac{2{{\text{x}}^{3}}-7{{\text{x}}^{2}}-12\text{x}+45}{3{{\text{x}}^{3}}-19{{\text{x}}^{2}}+33\text{x}-9}\)
