So far, we have operated on two or more fractions to make a single fraction.
Can we decompose a fraction into the sum or difference of two algebraic fractions?
1. Fill in the blanks with positive integers.
a)
$13$/$15$
$=$
/$3$
$+$
/$5$
b)
$13$/$28$
$=$
/$4$
$-$
/$7$
c)
$2x+6$/$3x$
$=$
/$3$
$+$
/$x$
d)
$-8x+35$/$10x$
$=$
/$2x$
$-$
/$5$
e)
$1+2x$/$x^2$
$=$
/$x$
$+$
/$x^2$
2. Fill in the blanks with positive integers.
a)
$9x+5$/$x\left(x+1\right)$
$=$
/$x$
$+$
/$x+1$
b)
$5x-4$/$\left(x-2\right)\left(x+1\right)$
$=$
/$x-2$
$+$
/$x+1$
3. Fill in the blanks with integers (may be positive or negative).
a)
$x+5$/$\left(x-3\right)\left(x+1\right)$
$=$
/$x-3$
$+$
/$x+1$
b)
$-8x+30$/$\left(2x-3\right)\left(x-6\right)$
$=$
/$2x-3$
$+$
/$x-6$
4. Fill in the blanks with integers (may be positive or negative).