a/ (x-1)²-(4x+3)(2-x)=x²-2x+1-(8x-4x²+6-3x)

=x²-2x+1-8x+4x²-6+3x=5x²-7x-6

b/ (15x³y² - 6x²y³) : 3x²y² = 5x - 2y

c/ \(\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{x^2-49}\)=\(\dfrac{\left(x+7\right)^2-\left(x-7\right)^2+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{x^2+14x+49-\left(x^2-14x+49\right)+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{28x+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{4x\left(x+7\right)}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{4x}{x-7}\)

\(1,\\ a,=xy^2-\dfrac{3}{2}y^3+\dfrac{5}{4}x^2\\ b,=\left(x-7\right)\left(x+7\right):\left(x-7\right)=x+7\\ 2,\dfrac{1}{a^2}-ab=\dfrac{1-a^3b}{a^2};\dfrac{1}{a^2}\text{ giữ nguyên}\\ 3,=\dfrac{-7}{t}\\ 4,=\dfrac{1-x+1-y}{x-y}=\dfrac{2-x-y}{x-y}\)

Bài 1:

\(a,\left(16x^3y^2-24x^2y^3+20x^4\right):16x^2=16x^2\left(xy^2-\dfrac{3}{2}y^3+\dfrac{5}{4}x^2\right):16x^2=xy^2-\dfrac{3}{2}y^3+\dfrac{5}{4}x^2\)

\(b,\left(x^2-49\right):\left(x-7\right)=\left[\left(x-7\right)\left(x+7\right)\right]:\left(x-7\right)=x+7\)

Bài 2:

\(\dfrac{1}{a^2}-ab=\dfrac{1-a^2b}{a^2}\)

\(\dfrac{1}{a^2}\)

Bài 3:

\(\dfrac{7\left(t-z\right)}{t\left(z-t\right)}=\dfrac{-7\left(z-t\right)}{t\left(z-t\right)}=\dfrac{-7}{t}\)

Bài 4:

\(\dfrac{x-1}{y-x}+\dfrac{1-y}{x-y}=\dfrac{x-1}{y-x}-\dfrac{1-y}{y-x}=\dfrac{x-1-1+y}{y-x}=\dfrac{x+y-2}{y-x}\)

a) Ta có: \(\dfrac{x}{x-3}-\dfrac{6}{x}-\dfrac{9}{x^2-3x}\)

\(=\dfrac{x^2}{x\left(x-3\right)}-\dfrac{6\left(x-3\right)}{x\left(x-3\right)}-\dfrac{9}{x\left(x-3\right)}\)

\(=\dfrac{x^2-6x+18-9}{x\left(x-3\right)}\)

\(=\dfrac{\left(x-3\right)^2}{x\left(x-3\right)}=\dfrac{x-3}{x}\)

b) Ta có: \(\dfrac{7}{x}-\dfrac{x}{x+6}+\dfrac{36}{x^2+6x}\)

\(=\dfrac{7\left(x+6\right)-x^2+36}{x\left(x+6\right)}\)

\(=\dfrac{7x+42-x^2+36}{x\left(x+6\right)}\)

\(=\dfrac{-\left(x^2-7x-78\right)}{x\left(x+6\right)}\)

\(=\dfrac{-\left(x^2-13x+6x-78\right)}{x\left(x+6\right)}\)

\(=\dfrac{-\left[x\left(x-13\right)+6\left(x-13\right)\right]}{x\left(x+6\right)}\)

\(=\dfrac{13-x}{x}\)

c) Ta có: \(\dfrac{6}{x-3}-\dfrac{2x-6}{x^2-9}-\dfrac{4}{x+3}\)

\(=\dfrac{6\left(x+3\right)-2x+6-4\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{6x+18-2x+6-4x+12}{\left(x-3\right)\left(x+3\right)}=\dfrac{36}{\left(x-3\right)\left(x+3\right)}\)

a: Sửa đề: \(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)

ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne9\end{matrix}\right.\)

Để A là số nguyên thì \(\sqrt{x}+1⋮\sqrt{x}-3\)

=>\(\sqrt{x}-3+4⋮\sqrt{x}-3\)

=>\(4⋮\sqrt{x}-3\)

=>\(\sqrt{x}-3\in\left\{1;-1;2;-2;4;-4\right\}\)

=>\(\sqrt{x}\in\left\{4;2;5;1;7;-1\right\}\)

=>\(\sqrt{x}\in\left\{4;2;5;1;7\right\}\)

=>\(x\in\left\{16;4;25;1;49\right\}\)

b: 

\(=\dfrac{x+7}{\left(x-3\right)\left(x+2\right)}+\dfrac{x+10}{\left(x+2\right)\left(x-1\right)}+\dfrac{x-7}{\left(x-1\right)\left(x-3\right)}\)

\(=\dfrac{x^2+6x-7+x^2+7x-30+x^2-5x-14}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}\)

\(=\dfrac{3x^2+8x-51}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}\)

\(=\dfrac{3x^2-9x+17x-51}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}=\dfrac{\left(3x+17\right)}{\left(x-1\right)\left(x+2\right)}\)

\(a,đk:x\ne0;4;1\)

\(\dfrac{x-1}{x^2-5x+4}-\dfrac{4}{x^2-4x}\\ =\dfrac{x-1}{\left(x-1\right)\left(x-4\right)}-\dfrac{4}{x\left(x-4\right)}\\ =\dfrac{x\left(x-1\right)}{x\left(x-1\right)\left(x-4\right)}-\dfrac{4\left(x-1\right)}{x\left(x-1\right)\left(x-4\right)}\\ =\dfrac{x^2-x-4x+4}{x\left(x-1\right)\left(x-4\right)}\\ =\dfrac{x^2-5x+4}{x.\left(x-1\right)\left(x-4\right)}=\dfrac{\left(x-1\right)\left(x-4\right)}{x.\left(x-1\right)\left(x-4\right)}=\dfrac{1}{x}\)

\(đk:x\ne-2;1\)

\(\dfrac{x}{x+2}+\dfrac{7x-16}{\left(x+2\right)\left(7x-7\right)}\\ =\dfrac{x\left(7x-7\right)}{\left(x+2\right)\left(7x-7\right)}+\dfrac{7x-16}{\left(x+2\right)\left(7x-7\right)}\\ =\dfrac{7x^2-7x+7x-16}{\left(x+2\right)\left(7x-7\right)}\\ =\dfrac{7x^2-16}{\left(x+2\right)\left(7x-7\right)}\)

a)

\(\dfrac{x-1}{x^2-5x+4}-\dfrac{4}{x^2-4x}\) \(ĐKXĐ:x\ne0;x\ne4;x\ne1\)

\(=\dfrac{x-1}{x^2-4x-x+4}-\dfrac{4}{x\left(x-4\right)}\)

\(=\dfrac{x-1}{x\left(x-4\right)-\left(x-4\right)}-\dfrac{4}{x\left(x-4\right)}\)

\(=\dfrac{x-1}{\left(x-1\right)\left(x-4\right)}-\dfrac{4}{x\left(x-4\right)}\)

\(=\dfrac{x^2-x}{x\left(x-1\right)\left(x-4\right)}-\dfrac{4\left(x-1\right)}{x\left(x-1\right)\left(x-4\right)}\)

\(=\dfrac{x^2-x-4x+4}{x\left(x-1\right)\left(x-4\right)}\)

\(=\dfrac{x\left(x-1\right)-4\left(x-1\right)}{x\left(x-1\right)\left(x-4\right)}\)

\(=\dfrac{\left(x-1\right)\left(x-4\right)}{x\left(x-1\right)\left(x-4\right)}\\ =\dfrac{1}{x}\)

b)

\(\dfrac{x}{x+2}+\dfrac{7x-16}{\left(x+2\right)\left(7x-7\right)}\)  \(ĐKXĐ:x\ne-2;x\ne1\)

\(=\dfrac{x\left(7x-7\right)}{\left(x+2\right)\left(7x-7\right)}+\dfrac{7x-16}{\left(x+2\right)\left(7x-7\right)}\)

\(=\dfrac{7x^2-7x+7x-16}{\left(x+2\right)\left(7x-7\right)}\)

\(=\dfrac{7x^2-16}{\left(x+2\right)\left(7x-7\right)}\)

a: =5x^3-5x^2y+5x-2x^2y+2xy^2-2y

=5x^3-7x^2y+2xy^2+5x-2y

b: =(x^2-1)(x+2)

=x^3+2x^2-x-2

c: =1/2x^2y^2(4x^2-y^2)

=2x^4y^2-1/2x^2y^4

d: =(x^2-1/4)(4x-1)

=4x^3-x^2-x+1/4

e: =x^2-2x-35+(2x+1)(x-3)

=x^2-2x-35+2x^2-6x+x-3

=3x^2-7x-38