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How to Simplify Algebraic Fractions

How would you simplify this, x squared plus x over x plus 1 times x plus three. First thing to notice is the denominator is already factorized but what about the numerator? What can you remove from both x squared and x?
Did you think of taking out x from both terms. That would give you x(x+1).
Can you see something to cancel between numerator and denominator? Remember now we just have one term top and bottom so we can cancel the x plus one. That leaves us with x on the top and x+3 on the bottom. We can leave out the parenthesis on the bottom now because the x plus three isn’t been multiplied by anything. At this point some students will seat there wondering if they could cancel those x’s top and bottom as well. There is one term on the top and two on the bottom so that can’t be done so the answer is x over x plus three.

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