How do you divide \frac { 5a ^ { 2} + 49a - 10} { 14a ^ { 2} + 30a + 4} \div \frac { 5a ^ { 2} - 51a + 10} { 14a ^ { 2} + 30a + 4}5a2+49a−1014a2+30a+4÷5a2−51a+1014a2+30a+4?

1 Answer
Andrew I.
Jan 16, 2018

(a+10)/(a-10)a+10a−10

Explanation:

To begin flip the second fraction upside-down to turn the divide into a multiply:

(5a^2+49a-10)/(14a^2+30a+4)divide(5a^2-51a+10)/(14a^2+30a+4)5a2+49a−1014a2+30a+4÷5a2−51a+1014a2+30a+4

=(5a^2+49a-10)/(14a^2+30a+4)times(14a^2+30a+4)/(5a^2-51a+10)=5a2+49a−1014a2+30a+4×14a2+30a+45a2−51a+10

Straight away we can cancel the denominator of the first with the numerator of the second like so:

=(5a^2+49a-10)/cancel(14a^2+30a+4)timescancel(14a^2+30a+4)/(5a^2-51a+10)

=(5a^2+49a-10)/1times1/(5a^2-51a+10)

=(5a^2+49a-10)/(5a^2-51a+10)

These polynomials can be factorised:

5a^2+49a-10=(5a-1)(a+10)

and

5a^2-51a+10=(5a-1)(a-10)

So the fraction now becomes:

=(5a^2+49a-10)/(5a^2-51a+10)=((5a-1)(a+10))/((5a-1)(a-10))

We can now cancel the 5a-1 to leave us with:

(cancel((5a-1))(a+10))/(cancel((5a-1))(a-10))=(a+10)/(a-10)

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