Một số bài tập về Rút gọn phân thức Toán 8 năm 2019

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) $\frac{x^2-xy}{3\text{x}y-3y^2}(x\ne y,y\ne 0)$

        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) $\frac{m^4-m}{2m^2+2m+2}$                                               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) $\frac{a^3+1}{2a^2+4a+2}$                                       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) $\frac{3x^3-2x^2+4x-5}{6x^2+3x-9}$                                            l) $\frac{x|x-2|}{x^2-5x+6}$

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) $\frac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}$;

u) $\frac{x^3-y^3+z^3+3xyz}{{(x+y)}^2+{(y+z)}^2+{(z-x)}^2}\text{(};ư)\text{(}\frac{x^3+y^3+z^3-3xyz}{{(x-y)}^2+{(y-z)}^2+{(z-x)}^2}$

Bài 3: Rút gọn, rồi tính giá trị các phân thức sau:

a) $A=\frac{(2{\text{x}}^2+2\text{x}){(x-2)}^2}{(x^3-4\text{x})(x+1)}\text{(}với\text{(}x=\frac{1}{2}$                     

b) $B=\frac{x^3-x^{2}y+x{y}^2}{x^3+y^3}\text{(}với\text{(}x=-5,y=10$

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) $\frac{2{\text{x}}^3-7{\text{x}}^2-12\text{x}+45}{3{\text{x}}^3-19{\text{x}}^2+33\text{x}-9}$