Question Video: Simplifying Algebraic Fractions

Find the quotient of (βˆ’43π‘₯⁷ + 12π‘₯Β³ βˆ’ 6π‘₯Β²)/π‘₯.

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Video Transcript

Find the quotient of negative 43π‘₯ to the power of seven plus 12π‘₯ cubed minus six π‘₯ squared divided by π‘₯.

In order to answer this question, we need to divide each of the terms by π‘₯: negative 43π‘₯ to the power of seven divided by π‘₯, 12π‘₯ cubed divided by π‘₯, and negative six π‘₯ squared divided by π‘₯.

Using the fact that π‘₯ is the same as π‘₯ to the power of one along with our laws of indices, π‘₯ to the power of π‘Ž divided by π‘₯ to the power of 𝑏 equals π‘₯ to the power of π‘Ž minus 𝑏 helps us work out that negative 43π‘₯ to the power of seven divided by π‘₯ is equal to negative 43π‘₯ to the power of six.

In the same way, 12π‘₯ cubed divided by π‘₯ is equal to 12π‘₯ squared. And finally, negative six π‘₯ squared divided by π‘₯ is equal to negative six π‘₯. Putting these three terms back together gives us an answer of negative 43π‘₯ to the power of six plus 12π‘₯ squared minus six π‘₯.

This means that the quotient of negative 43π‘₯ to the seven plus 12π‘₯ cubed minus six π‘₯ squared divided by π‘₯ is negative 43π‘₯ to the power of six plus 12π‘₯ squared minus six π‘₯.

You will notice that the exponents or indices in our answer are one less than the exponents in the question. This is because we are dividing by π‘₯ or π‘₯ to the power of one. Had we been dividing by π‘₯ squared, we would’ve reduced the exponents by two. And in the same way, dividing by π‘₯ cubed would reduce the exponents by three.

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