How do you simplify $\frac{\frac{x^{2} - 25}{x^{2} + 6 + 5}}{\frac{x}{x^{2}}}$ $((x^2-25 )/(x^2+6+5))/(x / x^2)$ ?

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How do you simplify $\frac{\frac{x^{2} - 25}{x^{2} + 6 + 5}}{\frac{x}{x^{2}}}$ $((x^2-25 )/(x^2+6+5))/(x / x^2)$ ?

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Answer 1 · 2016-07-27T12:06:42

$\frac{x (x - 5)}{(x + 1)}$ $(x(x-5))/((x+1))$

Explanation:

In this form, the fraction just looks nasty!!

We can write $\frac{\frac{a}{b}}{\frac{c}{d}}$ $(color(red)a/color(blue)b)/(color(blue)c/color(red)d)$ in the much easier form of $\frac{a \times d}{b \times c}$ $color(red)(axxd)/color(blue)(bxxc)$

Let's do the same for $\frac{\frac{x^{2} - 25}{x^{2} + 6 + 5}}{\frac{x}{x^{2}}}$ $(color(red)(x^2-25 )/color(blue)(x^2+6+5))/color(blue)(x / color(red)(x^2))$

= $\frac{(x^{2} - 25) \times x^{2}}{(x^{2} + 6 + 5) \times x} Much better!$ $color(red)((x^2-25 )xx x^2)/color(blue)((x^2+6+5)xx x)" Much better!"$

Now factorise and cancel like factors.

= $\frac{(x + 5) (x - 5) \times x^{2}}{(x + 5) (x + 1) \times x}$ $color(red)(((x+5)(x-5)xx x^2)/color(blue)((x+5)(x+1)xx x)$

= $(cancel(x+5)(x-5)xx x^cancel2)/(cancel(x+5)(x+1)xx cancelx)$

= $(x(x-5))/((x+1))$

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How do you simplify $\frac{\frac{x^{2} - 25}{x^{2} + 6 + 5}}{\frac{x}{x^{2}}}$ $((x^2-25 )/(x^2+6+5))/(x / x^2)$ ?

1 Answer

Explanation:

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How do you simplify ((x^2-25 )/(x^2+6+5))/(x / x^2)x2−25x2+6+5xx2((x^2-25 )/(x^2+6+5))/(x / x^2)?

1 Answer

Explanation:

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How do you simplify $\frac{\frac{x^{2} - 25}{x^{2} + 6 + 5}}{\frac{x}{x^{2}}}$ $((x^2-25 )/(x^2+6+5))/(x / x^2)$ ?