e: \(\left\{{}\begin{matrix}\dfrac{1}{x}-\dfrac{1}{y}=1\\\dfrac{3}{x}+\dfrac{4}{y}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{3}{y}=3\\\dfrac{3}{x}+\dfrac{4}{y}=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{-7}{y}=-2\\\dfrac{1}{x}-\dfrac{1}{y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{7}{2}\\\dfrac{1}{x}=1+\dfrac{2}{7}=\dfrac{9}{7}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{7}{2}\\x=\dfrac{7}{9}\end{matrix}\right.\)

vd câu 1:
ta có x-y=4 =>x=4+y
ta có pt:
4+y/y-2=3/2
=>8+2y=3y-6
=>-y=-14
=>y=14
=>x=4+y=4+14=18
các bài khác cũng tương tự thôi bạn

dấu chéo có nghĩa là phân số hí

a: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x+1+1}{x+1}+\dfrac{2}{y-2}=6\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+1}+\dfrac{2}{y-2}=5\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\)

=>x+1=1 và y-2=1/2

=>x=0 và y=5/2

b: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x-2y}=\dfrac{1}{2}-\dfrac{1}{18}=\dfrac{9}{18}-\dfrac{1}{18}=\dfrac{8}{18}=\dfrac{4}{9}\\\dfrac{2}{2x-y}=\dfrac{1}{18}+\dfrac{1}{x-2y}\end{matrix}\right.\)

=>x-2y=9 và 2/2x-y=1/18+1/9=1/18+2/18=3/18=1/6

=>x-2y=9 và 2x-y=12

=>x=5; y=-2

c: \(\Leftrightarrow\left\{{}\begin{matrix}10\left|x-6\right|+15\left|y+1\right|=25\\10\left|x-6\right|-8\left|y+1\right|=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23\left|y+1\right|=23\\\left|x-6\right|=1\end{matrix}\right.\)

=>|x-6|=1 và |y+1|=1

=>\(\left\{{}\begin{matrix}x\in\left\{7;5\right\}\\y\in\left\{0;-2\right\}\end{matrix}\right.\)

\(\dfrac{4x^2\left(y+z\right)^5}{2x\left(y+z\right)^3}=2x\left(y+z\right)^2\)

1) x² + x - y² + y = (x² - y²) + (x + y) = (x - y)(x + y) + (x + y) = (x - y + 1)(x + y)

2) 4x² - 9y² + 4x - 6y = (4x² - 9y²) + (4x - 6y) = (2x - 3y)(2x + 3y) + 2(2x - 3y) = (2x - 3y)(2x + 3y + 2)

3) x² + x + y² + y + 2xy = (x² + 2xy + y²) + (x + y) = (x + y)² + (x + y) = (x + y)(x + y + 1)

4) -x² + 5x + 2xy - 5y - y² = -(x² - 2xy + y²) + (5x - 5y) = -(x - y)² + 5(x - y) = (x - y)(y - x + 5)

5) x² - y² + 2x + 1  = (x² + 2x + 1) - y² = (x + 1)² - y² = (x + 1 + y)(x - y + 1)

6) x² - 1 - y² + 2y = x² - (y² - 2y + 1) = x² - (y - 1)² = (x - y + 1)(x + y - 1)

7) x² + 2xz - y² + 2uy + z² - u² =(x² + 2xz + z²) - (y² - 2uy + u²) = (x + z)² - (y - u)² = (x + z - y + u)(x + z + y - u)

8) x³ + 3x²y + x + 3xy² + y + y³ = (x³ + 3x²y + 3xy² + y³) + (x + y) = (x + y)³ + (x + y) = (x + y)(x² + 2xy + y² + 1)

9) x³ + y(1 - 3x²) + x(3y² - 1) - y³ = x³ + y - 3x²y + 3xy² - x - y³ = (x³ - 3x²y + 3xy² - y³) - (x - y) = (x - y)³ - (x - y) = (x - y)(x² - 2xy+y²-1)

a) Ta có: \(\left\{{}\begin{matrix}\dfrac{5}{x-1}+\dfrac{1}{y-1}=10\\\dfrac{1}{x-1}-\dfrac{3}{y-1}=18\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5}{x-1}+\dfrac{1}{y-1}=10\\\dfrac{5}{x-1}-\dfrac{15}{y-1}=90\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{16}{y-1}=-80\\\dfrac{1}{x-1}-\dfrac{3}{y-1}=18\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y-1=\dfrac{-1}{5}\\\dfrac{1}{x-1}=18+\dfrac{3}{y-1}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{4}{5}\\x-1=\dfrac{1}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{4}{3}\\y=\dfrac{4}{5}\end{matrix}\right.\)

\(2x^2y^3+5y^2x^3+\left(-\dfrac{1}{2}x^3y^2\right)+\left(-\dfrac{1}{2}x^2y^3\right)\\ =\left[2x^2y^3+\left(-\dfrac{1}{2}x^2y^3\right)\right]+\left[5x^3y^2+\left(-\dfrac{1}{2}x^3y^2\right)\right]\\ =\dfrac{3}{2}x^2y^3+\dfrac{9}{2}x^3y^2\)