FRACTION ALGEBRA
Common fraction mistakes: grouping, cancellation and zero denominators
Examples checked with MathTexLab’s base and AMS math renderer · Display style
A fraction can be valid LaTeX and still be the wrong mathematical expression. The builder handles notation; you must check algebra, assumptions and the quantities that belong above and below the bar.
Keep added terms in the right place
\frac{x+1}{x} means that the entire sum x plus one is divided
by x. x+\frac{1}{x} places the first x outside the fraction.
Enter the intended full numerator in its field rather than appending a term
after the generated quotient.
Cancel factors, not pieces of a sum
You cannot cancel the x in \frac{x+1}{x} to obtain 1+1. A
factor can cancel when it multiplies the whole numerator and denominator. In
this example, the displayed equality requires the original restriction x not
equal to zero.
\frac{x(x+1)}{x}=x+1\quad(x\ne 0)Record denominator restrictions
A zero denominator can be typeset, but division by zero is undefined in ordinary arithmetic. Likewise, after cancelling a factor you must retain any restriction from the original denominator. The Fraction Generator does not enforce domains, solve equations or certify identities.
Verify in two passes
First read the source and preview to check grouping, signs and exponent positions. Then check the mathematics separately. Use the editor to add conditions beside an expression and export the result only when both passes are complete. An error message identifies a rendering problem; a ready preview is not an algebra validation result.
Syntax reference
MathJax supported-command reference. The examples above are limited to the features described here; additional packages are not implied.
Continue with LaTeX Fraction Generator.