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Adding & subtracting rational expressions: like denominators

Video transcript

so let's add six over 2x squared minus seven to negative 3x minus eight over 2x squared minus seven and like always pause the video and try to work it out before I do well when you look at this we have these two rational expressions and we have the same denominator 2x squared minus 7 so you could say we have 6 2x squared minus 7 and then we have negative 3x minus 8 2x squared minus 7 is one way to think about it so if you have the same denominator this is going to be equal to this is going to be equal to our denominator is going to be 2x squared minus 7 - x squared minus 7 and then we just add the numerators so it's going to be 6 plus negative 3x negative 3x minus 8 and so if we want to simplify this a little bit we'd recognize that we can add these two constant terms the 6 and the negative 8 6 plus negative 8 is going to be negative 2 so it's going to be negative 2 and then adding a negative 3x that's the same thing as subtracting 3x so negative 2 minus 3x all of that over all of that that same blue color all of that over 2x squared minus 7 and we're done we've just added these two rational expressions let's do another example so here we want to subtract one rational expression from another so see if you can figure that out well once again both of these rational expressions have the exact same denominator the denominator for both of them is 14x squared minus 9 14x squared minus 9 so the denominator of the difference things we can call it that is going to be 14x squared minus 9 so 14x squared minus 9 did I say 4x squared before 14 x squared minus 9 that's the denominator both of them so that's going to be the dominant denominator of our answer right over here and so we can just subtract the numerators so we're going to have 9x squared plus 3 minus - all of this business - negative three x squared plus five and so we can distribute the negative sign this is going to be equal to this is going to be equal to nine x squared plus three and then if you distribute the negative sign the negative of negative 3x squared is going to be plus three x squared and then the negative of positive five it's going to be negative five so we're going to subtract five from that and all of that is going to be over fourteen x squared minus nine fourteen x squared minus nine and so in the numerator we can do some simplification we have nine x squared plus three x squared so that's going to be equal to twelve x squared and then we have we have three plus negative five we're going to say three minus five so that's going to be negative two and all of that is going to be over fourteen x squared minus nine fourteen x squared minus nine and we're all done we have just subtracted and we could think about is there any way to simplify this more are there any common factors but these both could be considered differences of squares but they're going to be differences of squares of of different things so they're not going to have common factors so this is about as simple as we can get