Question

Tính giá trị biểu thức: N=3x-5/2x+y - 4y+5/x+3y với x-y=5

Answer 1

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

\(=\dfrac{3x^2+9xy-5x-15y-8xy-4y^2-10x-5y}{\left(x+3y\right)\left(2x+y\right)}\)

\(=\dfrac{3x^2+xy-15x-20y-4y^2}{\left(x+3y\right)\left(2x+y\right)}\)

x-y=5 nên x=y+5

\(N=\dfrac{3\left(y+5\right)^2+y\left(y+5\right)-15\left(y+5\right)-20y-4y^2}{\left(y+5+3y\right)\left[2\left(y+5\right)+y\right]}\)

\(=\dfrac{3y^2+30y+75+y^2+5y-15y-75-20y-4y^2}{\left(4y+5\right)\left(y+10\right)}\)

\(=\dfrac{15y}{\left(4y+5\right)\left(y+10\right)}\)