How do you simplify $\frac{8 x}{x^{2} - 9 x + 14} \div \frac{x^{2} + 5 x}{x^{2} - 4} \div \frac{x + 2}{x - 7}$ $\frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}$ ?

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How do you simplify $\frac{8 x}{x^{2} - 9 x + 14} \div \frac{x^{2} + 5 x}{x^{2} - 4} \div \frac{x + 2}{x - 7}$ $\frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}$ ?

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Answer 1 · 2017-08-09T11:08:38

$\frac{8}{x + 5}$ $8/(x+5$

Explanation:

First, we get rid of the division symbols by turning them into multiplication by getting the reciprocal of the fraction, giving us a new equation of

$\frac{8 x}{x^{2} - 9 x + 14} \times \frac{x^{2} - 4}{x^{2} + 5 x} \times \frac{x - 7}{x + 2}$ $(8x)/(x^2-9x+14)times(x^2-4)/(x^2+5x)times(x-7)/(x+2)$

We then factorise all the values we can to their simplest form, giving us

$\frac{8 x}{(x - 7) (x - 2)} \times \frac{(x - 2) (x + 2)}{x (x + 5)} \times \frac{x - 7}{x + 2}$ $(8x)/((x-7)(x-2))times((x-2)(x+2))/(x(x+5))times(x-7)/(x+2)$

We then get rid of common factors, simplifying the equation down to

$\frac{8}{1} \times \frac{1}{(x + 5)} \times \frac{1}{1}$ $(8)/1times1/((x+5))times1/1$

Giving us the answer of

$\frac{8}{x + 5}$ $8/(x+5$

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How do you simplify $\frac{8 x}{x^{2} - 9 x + 14} \div \frac{x^{2} + 5 x}{x^{2} - 4} \div \frac{x + 2}{x - 7}$ $\frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}$ ?

1 Answer

Explanation:

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How do you simplify 8xx2−9x+14÷x2+5xx2−4÷x+2x−7\frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}?

1 Answer

Explanation:

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How do you simplify $\frac{8 x}{x^{2} - 9 x + 14} \div \frac{x^{2} + 5 x}{x^{2} - 4} \div \frac{x + 2}{x - 7}$ $\frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}$ ?