Write each rational expression in lowest terms. m^2 - 4m + 4 / m^...

Question

Write each rational expression in lowest terms. m^2 - 4m + 4 / m^2 + m - 6

Accepted Answer

Hello, everyone. We're going to completely reduce the rational expression, Y squared minus 10, Y plus 25 over Y squared plus Y minus 30 to its simplest form. First thing I want to do is rewrite this. So my expressions are one over another. So I'll have Y squared minus 10, Y plus 25 over Y squared plus Y minus 30. So I recall that when I want to simplify a rational expression, I can't break up addition and subtraction. So I need to factor my, try no meals. So in the numerator, I'm gonna break it into two sets of dino meals. And I recall that I want to find a value that will multiply to a positive, But add to a negative 10. So my first term in each is still gonna be why? So multiplying to a positive 25 but adding to a negative 10 would be negative five and negative five. So why squared minus 10, Y plus 25 would factor two Y minus five times Y minus five in the denominator. Again, the wives are going to be the first term in each set of dino meals or each set of parentheses. And then I need two numbers that multiply to a negative 30 but add to a positive one. So would multiply the negative 30 but add to positive one would be negative five and positive six. So Y squared plus Y minus 30 would factor to why minus five times Y plus six. Now, I recognize that I do have all of this broken into factors so I can reduce And I can reduce why -5 with Y -5. So one from the numerator and one from the denominator. And at this point, I'm left with Y minus five over Y plus six. There's nothing else I can do to reduce that. So that is my final expression. So Y minus five over Y plus six because I can't break up addition or subtraction. So those wives can't go anywhere. And that would be answer choice. C have a nice day.

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Write each rational expression in lowest terms. m^2 - 4m + 4 / m^2 + m - 6