if a=4x/3y and b=3x/4y,find the value of (a+1/b)×(b+1/a).
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if , a=4x/3y,b=3x/4y
then,
a+1/b*b+1/a
=4x/3y+1/3x/4y*3x/4y+1/4x/3y
=4x/3y+4y/3x*3x/4y+3y/4x
=4x^2+4y^2/9xy*3x^2+3y^2/16xy
=12x^4+12y^4×24x^2y2/144x^2y^2
=x^4+y^4+2x^2y^/12x^2y^2
then,
a+1/b*b+1/a
=4x/3y+1/3x/4y*3x/4y+1/4x/3y
=4x/3y+4y/3x*3x/4y+3y/4x
=4x^2+4y^2/9xy*3x^2+3y^2/16xy
=12x^4+12y^4×24x^2y2/144x^2y^2
=x^4+y^4+2x^2y^/12x^2y^2
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