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Math Help - Please explainhow did he simplified this given?

  1. #1
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    Please explainhow did he simplified this given?

    Hi, Can you please show me the step-by-step process of this example. Especially the second and third line?


    Here is the given:
    (xy-x)dx=(x^2y^2-x^2)+(y^2-1)dy
    x(y-1)dx=(x^2(y^2-1)+(y^2-1))dy
    =(x^2+1)(y^2-1)dy
    xdx=(x^2+1)(y+1)dy


    Any help will be appreciated, thanks
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  2. #2
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    Quote Originally Posted by davewhite123 View Post
    Hi, Can you please show me the step-by-step process of this example. Especially the second and third line?


    Here is the given:
    (xy-x)dx=(x^2y^2-x^2)+(y^2-1)dy
    x(y-1)dx=(x^2(y^2-1)+(y^2-1))dy
    =(x^2+1)(y^2-1)dy
    xdx=(x^2+1)(y+1)dy


    Any help will be appreciated, thanks
    (xy-x)dx=(x^2y^2-x^2)+(y^2-1)dy

    x is a common factor of xy and x, so xy-x=x(y-1)

    x^2 is a common factor of x^2y^2 and x^2, so x^2y^2-x^2=x^2(y^2-1)

    Now y^2-1 is a common factor, so x^2(y^2-1)+(y^2-1)=(y^2-1)(x^2+1)

    Finally, y^2-1=(y+1)(y-1)

    hence y-1 is common to both sides and can be eliminated to obtain the last line.
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