document.write( "Question 30566: Let f(x)=x2+x and g(x)=x+1. Find each of the following:\r
\n" ); document.write( "\n" ); document.write( "(f+g)(x) (f.g)(x) (f divided by (g)(x) \n" ); document.write( "

Algebra.Com's Answer #17226 by sdmmadam@yahoo.com(530) $\"\"$ $\"About$

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f(x)=x^2+x ----(1)
\n" ); document.write( "g(x)=x+1 ----(2)
\n" ); document.write( "Both (1) and (2) are defined for all real x
\n" ); document.write( "To find (f+g)(x) (f.g)(x) (f divided by (g)(x)
\n" ); document.write( "1) (f+g)(x) = f(x)+g(x)
\n" ); document.write( "= (x^2+x)+(x+1) using (1) and (2)
\n" ); document.write( "=x^2+(x+x)+1
\n" ); document.write( "= x^2+2x+1\r
\n" ); document.write( "\n" ); document.write( "2)(f.g)(x) = f(x).g(x)
\n" ); document.write( "= (x^2+x)(x+1) using (1) and (2)
\n" ); document.write( "=x^2(x+1)+x(x+1)
\n" ); document.write( "= (x^3+x^2)+(x^2+x)
\n" ); document.write( "= x^3+(x^2+x^2)+x
\n" ); document.write( "=x^3+2x^2+x\r
\n" ); document.write( "\n" ); document.write( "3)(f/g)(x) = f(x)/g(x) (for g(x) not zero)
\n" ); document.write( "= (x^2+x)/(x+1) [defined for x not equal to (-1)]
\n" ); document.write( "= x(x+1)/(x+1) (for x not equal to (-1))
\n" ); document.write( "= x (cancelling (x+1) not zero )\r
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