In the second step we acknowledged that a minus sign

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Unformatted text preview: fact on the second term in the denominator. a - b = - (b - a ) OR - a + b = - ( a - b) This is commonly referred to as factoring a minus sign out because that is exactly what we’ve done. There are two forms here that cover both possibilities that we are liable to run into. In our case however we need the first form. Because of some notation issues let’s just work with the denominator for a while. x ( 5 - x ) = x é- ( x - 5)ù ë û = x é( -1)( x - 5 ) ù ë û = x ( -1)( x - 5 ) = ( -1)( x )( x - 5 ) = - x ( x - 5) Notice the steps used here. In the first step we factored out the minus sign, but we are still multiplying the terms and so we put in an added set of brackets to make sure that we didn’t forget that. In the second step we acknowledged that a minus sign in front is the same as multiplication by “-1”. Once we did that we didn’t really need the extra set of brackets anymore so we dropped them in the third step. Next, we recalled that we change the order of a multiplication if we need...
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