Toán Lớp 10: Rút gọn x+√x/√x+x-1/√x+1-x-4/√x-2 Giúp minh vs.

Question

Toán Lớp 10:  Rút gọn  x+√x/√x+x-1/√x+1-x-4/√x-2 Giúp minh vs.

hothaibinh · Answer

Giải đáp:   $ begin{array}{l}  dfrac{{x +  sqrt x }}{{ sqrt x }} +  dfrac{{x - 1}}{{ sqrt x  + 1}} -  dfrac{{x - 4}}{{ sqrt x  - 2}}    =  dfrac{{ sqrt x  left( { sqrt x  + 1}  right)}}{{ sqrt x }} +  dfrac{{ left( { sqrt x  + 1}  right) left( { sqrt x  - 1}  right)}}{{ sqrt x  + 1}} -  dfrac{{ left( { sqrt x  - 2}  right) left( { sqrt x  + 2}  right)}}{{ sqrt x  - 2}}    =  sqrt x  + 1 +  sqrt x  - 1 -  left( { sqrt x  + 2}  right)    = 2 sqrt x  -  sqrt x  - 2    =  sqrt x  - 2  end{array}$

tuyetanhthu · Answer

#tnvt    frac{x+ sqrt{x}}{ sqrt{x}}+ frac{x-1}{ sqrt{x}+1}- frac{x-4}{ sqrt{x}-2}(x ne4,x>0)   = frac{ sqrt{x}( sqrt{x}+1)}{ sqrt{x}}+ frac{( sqrt{x}-1)( sqrt{x}+1)}{ sqrt{x}+1}- frac{( sqrt{x}-2)( sqrt{x}+2)}{ sqrt{x}-2}   = sqrt{x}+1+ sqrt{x}-1-( sqrt{x}+2)   =2 sqrt{x}- sqrt{x}-2   = sqrt{x}-2