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Ta có: \(\frac{\left(x^2\right)^2-10x^2+9}{x^4+6x^3+9x^2+2x^3+12x^2+18x+x^2+6x+9}\)
= \(\frac{\left(x^2-1\right)\left(x^2-3\right)}{x^2\left(x^2+6x+9\right)+2x\left(x^2+6x+9\right)+\left(x^2+6x+9\right)}\)
= \(\frac{\left(x-1\right)\left(x+1\right)\left(x-3\right)\left(x+3\right)}{\left(x^2+6x+9\right)\left(x^2+2x+1\right)}\)
= \(\frac{\left(x-1\right)\left(x+1\right)\left(x-3\right)\left(x+3\right)}{\left(x+3\right)^2.\left(x+1\right)^2}\)
= \(\frac{\left(x-1\right)\left(x+1\right)\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+3\right)\left(x+1\right)\left(x+1\right)}\)
= \(\frac{\left(x-1\right)\left(x-3\right)}{\left(x+1\right)\left(x+3\right)}\)
\(a)\frac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}=\frac{(x-3)^2(2x+5)}{(3x-1)(x-3)^2}(ĐK:x\ne3,x\ne\frac{1}{3})\)
\(=\frac{2x+5}{3x-1}\)
Còn bài b bạn tự làm nhé
Điều kiện: \(x\ne\left\{-1;-2;-5\right\}\)
\(\frac{x^3+x^2-4x-4}{x^3+8x^2+17x+10}=\frac{x^2\left(x+1\right)-4\left(x+1\right)}{x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)}\)
\(=\frac{\left(x+1\right)\left(x^2-4\right)}{\left(x+1\right)\left(x^2+7x+10\right)}\)
\(=\frac{\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x+1\right)\left[x\left(x+2\right)+5\left(x+2\right)\right]}\)
\(=\frac{\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+5\right)}=\frac{x-2}{x+5}\)
Điều kiện: \(x\ne\left\{3;\frac{1}{3}\right\}\)
\(\frac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}=\frac{2x^3-6x^2-x^2+3x-15x+45}{3x^3-9x^2-10x^2+30x+3x-9}\)
\(=\frac{2x^2\left(x-3\right)-x\left(x-3\right)-15\left(x-3\right)}{3x^2\left(x-3\right)-10x\left(x-3\right)+3\left(x-3\right)}\)
\(=\frac{\left(x-3\right)\left(2x^2-x-15\right)}{\left(x-3\right)\left(3x^2-10x+3\right)}\)
\(=\frac{2x^2-x-15}{3x^2-10x+3}=\frac{2x\left(x-3\right)+5\left(x-3\right)}{3x\left(x-3\right)-\left(x-3\right)}\)
\(=\frac{\left(2x+5\right)\left(x-3\right)}{\left(3x-1\right)\left(x-3\right)}=\frac{2x+5}{3x-1}\)
Bài 1:
a) \(\dfrac{15xy}{10x^2y}\)
= \(\dfrac{3.5xy}{2.5xyx}\)
= \(\dfrac{3}{2x}\)
d) \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)
= \(\dfrac{3.2x\left(x+5\right)\left(x+5\right)^2}{x.2x\left(x+5\right)}\)
= \(\dfrac{3\left(x+5\right)^2}{x}\)
a , \(16x^2+8x+1=\left(4x\right)^2+2.4x.1+1^2=\left(4x+1\right)^2\)
b , \(x^2-x+\dfrac{1}{4}=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x-\dfrac{1}{2}\right)^2\)
a,(4x+1)2 e,\(\left(\dfrac{3}{2}x-\dfrac{2}{5}\right)^2\)
b,(x-\(\dfrac{1}{2}\))2 g,\(\left(xy+1\right)^2\)
c,(\(x+\dfrac{3}{2}\))2 h,\(\left(x+5\right)^2\)
d,\(\left(x-\dfrac{5}{4}\right)^2\) i,\(-\left(x-6\right)^2\)
k,\(-\left(2x+3\right)^2\)
\(\dfrac{x^4-10x^2+9}{x^4+8x^3+22x^2+24x+9}\)
\(=\dfrac{x^4-x^2-9x^2+9}{x^4+x^3+7x^3+7x^2+15x^2+15x+9x+9}\)
\(=\dfrac{x^2\left(x^2-1\right)-9\left(x^2-1\right)}{x^3\left(x+1\right)+7x^2\left(x+1\right)+15x\left(x+1\right)+9\left(x+1\right)}\)
\(=\dfrac{\left(x^2-3^2\right)\left(x^2-1\right)}{\left(x+1\right)\left(x^3+7x^2+15x+9\right)}\)
\(=\dfrac{\left(x-3\right)\left(x+3\right)\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(x^3+x^2+6x^2+6x+9x+9\right)}\)
= \(\dfrac{\left(x+3\right)\left(x-3\right)\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left[x^2\left(x+1\right)+6x\left(x+1\right)+9\left(x+1\right)\right]}\)
= \(\dfrac{\left(x+3\right)\left(x-3\right)\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(x+1\right)\left(x^2+2.3x+3^2\right)}\)
= \(\dfrac{\left(x-3\right)\left(x-1\right)}{\left(x+1\right)\left(x+3\right)}\)