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เศษส่วนพหุนาม (Polynomial fractions) hard

Total questions: 11

Worksheet time: 3hrs 35mins

Name
Class
Date
1.

 2a2+103a2+15×a2+a2a2+2a \frac{2a^2+10^{ }}{3a^2+15}\times\frac{a^2+a}{2a^2+2a}\   

a)

 −1(−13)-1\left(\frac{-1}{3}\right)  

b)

 ∣−3a−6a∣\left|\frac{-3a}{-6a}\right|  

c)

 31\frac{3}{1}  

d)

 3a2+3a−33a^2+3a-3  

2.

 [7x2+7y212x2+12y2÷2x+2y3x+3y] ×2x21\left[\frac{7x^2+7y^2}{12x^2+12y^2}\div\frac{2x+2y}{3x+3y}\right]\ \times\frac{2x}{21}  

a)

 −y12\frac{-y}{12}  

b)

 x12\frac{x}{12}  

c)

 −x12\frac{-x}{12}  

d)

 y12\frac{y}{12}  

3.

   [3x3+3y3 2x3+2y3×3x2+3y22x2+2y2]+[7x+7y5x+5y÷3x2+3y22x2+2y2]\ \ \left[\frac{3x^3+3y^3\ }{2x^3+2y^3}\times\frac{3x^2+3y^2}{2x^2+2y^2}\right]+\left[\frac{7x+7y}{5x+5y}\div\frac{3x^2+3y^2}{2x^2+2y^2}\right]  

a)

 18060\frac{180}{60}  

b)

 19160\frac{191}{60}  

c)

 94+10\frac{9}{4}+10  

d)

 π\pi  

4.

 x2+16x2+8x+16+2x+16x2+64\frac{x^2+16}{x^2+8x+16}+\frac{2x+16}{x^2+64}  

a)

 44  

b)

 x−82\frac{x-8}{2}  

c)

16+x

d)

 2x+8\frac{2}{x+8}  

5.

     [x2−4x−32x2−5x−24×x2+7x+12(x+4)2]+[x2−x−30x2−11x−30×x2+x+30x2+11x+30][4x−202x+6÷2x−102x+6]+[4x2−122x2+6÷2x2−62x2+6]\ \ \ \ \frac{\left[\frac{x^2-4x-32}{x^2-5x-24}\times\frac{x^2+7x+12}{\left(x+4\right)^2}\right]+\left[\frac{x^2-x-30}{x^2-11x-30}\times\frac{x^2+x+30}{x^2+11x+30}\right]}{\left[\frac{4x-20}{2x+6}\div\frac{2x-10}{2x+6}\right]+\left[\frac{4x^2-12}{2x^2+6}\div\frac{2x^2-6}{2x^2+6}\right]}  

a)

 4412\frac{44}{12}  

b)

 72\frac{7}{2}  

c)

 12\frac{1}{2}  

d)

 0.60.6  

6.

 4(2x2−x−6)2(2x2−12x+16)×6(2x2−2x−24)3(2x2+9x+9)=2x+6(3x+6)2÷(x−3)2(12x+24)2\frac{4\left(2x^2-x-6\right)}{2\left(2x^2-12x+16\right)}\times\frac{6\left(2x^2-2x-24\right)}{3\left(2x^2+9x+9\right)}=\frac{2x+6}{\left(3x+6\right)^2}\div\frac{\left(x-3\right)^2}{\left(12x+24\right)^2}  

a)

 x=152x=\frac{15}{2}  

b)

 x=5x=5  

c)

 x=3x=3  

d)

 x=15x=15  

7.

 (2x−6)×(4x+12)2(5x−15)2×(3x+9)×(7x−49)2+(8x+56)(4x−28)×(2x+14)2=2−2xx−2×x2−5x+62x−6\frac{\left(2x-6\right)\times\left(4x+12\right)^2}{\left(5x-15\right)^2\times\left(3x+9\right)}\times\frac{\left(7x-49\right)^2+\left(8x+56\right)}{\left(4x-28\right)\times\left(2x+14\right)^2}=\frac{2-2x}{x-2}\times\frac{x^2-5x+6}{2x^{ }-6}  

a)

x=-1

b)

x=3

c)

x=-2

d)

x=4

8.

 44x+4+22x+2=\frac{4}{4x+4}+\frac{2}{2x+2}=  

a)

 2x−2\frac{2}{x-2}  

b)

 32(x+2)\frac{3}{2\left(x+2\right)}  

c)

 2x+1\frac{2}{x+1}  

d)

 22(x−2)\frac{2}{2\left(x-2\right)}  

9.

 (7x2−14)+(5x2−10)3x2−6=\frac{\left(7x^2-14\right)+\left(5x^2-10\right)}{3x^2-6}=  

a)

2

b)

4

c)

1

d)

3

10.

  เมื่อคำตอบของ x,y เป็นด้านข้ามเละชิดตามลำดับ จงหา cosec θ

a)

 cosec⁡θ=53\operatorname{cosec}\theta=\frac{5}{3}  

b)

 cosec⁡θ=35\operatorname{cosec}\theta=\frac{3}{5}  

c)

 cosec⁡θ=45\operatorname{cosec}\theta=\frac{4}{5}  

d)

 cosec⁡θ=54\operatorname{cosec}\theta=\frac{5}{4}  

11.

 x3=(2x2+2y9y+9x23)2x^3=^{ }\left(\frac{2x^2+2y}{\frac{9y+9x^2}{3}}\right)^2  

a)

 x=2323x=\frac{2}{3}^{\frac{2}{3}}  

b)

 x=3223x=\frac{3}{2}^{\frac{2}{3}}  

c)

 x=2332x=\frac{2}{3}^{\frac{3}{2}}  

d)

 x=3232x=\frac{3}{2}^{\frac{3}{2}}