# Writing ${{5-5\cdot x}\over{x}}+8\over{{1-x}\over{x}} + 1$ in one fraction

How do I write this expression in only one fraction:

$${{5-5\cdot x}\over{x}}+8\over{{1-x}\over{x}} + 1$$

I tried it several times but it somehow never worked! Thanks!

• Multiply top and bottom by $x$. – user61527 Dec 29 '13 at 22:22
• What should i do if x is not in both fractions? – John Smith Dec 29 '13 at 22:23
• Separately write the top part and the bottom part over a common denominator. Then use $\frac ab \div \frac cd = \frac ab \times \frac dc$. – Stephen Montgomery-Smith Dec 29 '13 at 22:24
• It is in both fractions isn't it? – okarin Dec 29 '13 at 22:24
• Sorry but could please somebody post the right solution as answer?Thanks – John Smith Dec 29 '13 at 22:27

$${{5-5\cdot x}\over{x}}+8=\frac{5-5x+8x}{x}$$
$$\frac{1-x}{x} + 1=\frac{1-x+x}{x}=\frac{1}{x}$$
${{5-5\cdot x}\over{x}}+8\over{{1-x}\over{x}} + 1$ $* \frac{x}{x} = \frac{5 - 5x + 8x}{1-x+x} = \frac{3x + 5}{1} = 3x+5,$ provided $x\not = 0$.
• A formula is not necessarily a recipe. There’s nothing wrong with the method sketched by @Listing, but @okarin’s method here will almost always be faster. Remember that top and bottom of a fraction may always be multiplied by the same nonzero quantity, and the fraction’s value will be unchanged. Here, the magic nonzero quantity is simply $x$, but in other cases you may have to look just a little deeper. – Lubin Dec 30 '13 at 4:22
$$\frac{\frac{5-5x}{x}+8}{\frac{1-x}{x} + 1}=\frac{\frac{5-5x+8x}{x}}{\frac{1-x+x}{x}}=\frac{\frac{5+3x}{x}}{\frac{1}{x}}=5+3x$$