document.write( "Question 388884: simplify the following expression:\r
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document.write( "(x^3+x^2-x-27)/(x^2-4x+3)\r
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document.write( "((x^5+x^2+16x-4)/(x^4-16))-(x/3) \n" );
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Algebra.Com's Answer #275287 by haileytucki(390)![]() ![]() You can put this solution on YOUR website! Are these seperate questions?? If so:\r \n" ); document.write( "\n" ); document.write( "(x^(3)+x^(2)-x-27)/(x^(2)-4x+3)\r \n" ); document.write( "\n" ); document.write( "In this problem -1*-3=3 and -1-3=-4, so insert -1 as the right hand term of one factor and -3 as the right-hand term of the other factor. \n" ); document.write( "(x^(3)+x^(2)-x-27)/((x-1)(x-3))\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "((x^(5)+x^(2)+16x-4)/(x^(4)-16))-((x)/(3))\r \n" ); document.write( "\n" ); document.write( "The binomial can be factored using the difference of squares formula, because both terms are perfect squares. \n" ); document.write( "((x^(5)+x^(2)+16x-4)/((x^(2)+4)(x^(2)-4)))-((x)/(3))\r \n" ); document.write( "\n" ); document.write( "The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b). \n" ); document.write( "((x^(5)+x^(2)+16x-4)/((x^(2)+4)(x-2)(x+2)))-((x)/(3))\r \n" ); document.write( "\n" ); document.write( "Multiply -1 by the (x)/(3) inside the parentheses. \n" ); document.write( "(x^(5)+x^(2)+16x-4)/((x^(2)+4)(x-2)(x+2))-(x)/(3)\r \n" ); document.write( "\n" ); document.write( "Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 3(x^(2)+4)(x+2)(x-2). The ((x^(5)+x^(2)+16x-4))/((x^(2)+4)(x-2)(x+2)) expression needs to be multiplied by ((3))/((3)) to make the denominator 3(x^(2)+4)(x+2)(x-2). The -(x)/(3) expression needs to be multiplied by ((x^(2)+4)(x+2)(x-2))/((x^(2)+4)(x+2)(x-2)) to make the denominator 3(x^(2)+4)(x+2)(x-2). \n" ); document.write( "(x^(5)+x^(2)+16x-4)/((x^(2)+4)(x-2)(x+2))*(3)/(3)-(x)/(3)*((x^(2)+4)(x+2)(x-2))/((x^(2)+4)(x+2)(x-2))\r \n" ); document.write( "\n" ); document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3(x^(2)+4)(x+2)(x-2). \n" ); document.write( "((x^(5)+x^(2)+16x-4)(3))/(3(x^(2)+4)(x+2)(x-2))-(x)/(3)*((x^(2)+4)(x+2)(x-2))/((x^(2)+4)(x+2)(x-2))\r \n" ); document.write( "\n" ); document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3(x^(2)+4)(x+2)(x-2). \n" ); document.write( "((x^(5)+x^(2)+16x-4)(3))/(3(x^(2)+4)(x+2)(x-2))-(x(x^(2)+4)(x+2)(x-2))/(3(x^(2)+4)(x+2)(x-2))\r \n" ); document.write( "\n" ); document.write( "The numerators of expressions that have equal denominators can be combined. In this case, ((x^(5)+x^(2)+16x-4)(3))/(3(x^(2)+4)(x+2)(x-2)) and -((x(x^(2)+4)(x+2)(x-2)))/(3(x^(2)+4)(x+2)(x-2)) have the same denominator of 3(x^(2)+4)(x+2)(x-2), so the numerators can be combined. \n" ); document.write( "((x^(5)+x^(2)+16x-4)(3)-(x(x^(2)+4)(x+2)(x-2)))/(3(x^(2)+4)(x+2)(x-2))\r \n" ); document.write( "\n" ); document.write( "Simplify the numerator of the expression. \n" ); document.write( "(2x^(5)+3x^(2)+64x-12)/(3(x^(2)+4)(x+2)(x-2)) \n" ); document.write( " |