How do you simplify $\frac{y + 2}{y^{2} + 2 y - 48} \div \frac{y + 2}{y^{2} - 13 y + 42}$ $(y+2) /(y^2+2y-48) div(y+2)/(y^2-13y+42 )$ ?

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Answer 1 · 2018-06-14T11:46:57

When dividing fractions we Keep Flip Change (KFC!)

Keep the first fraction the same

$\frac{y + 2}{y^{2} + 2 y - 48}$ $[y+2]/[y^2+2y-48]$

Flip the second fraction

$\frac{y^{2} - 13 y + 42}{y + 2}$ $[y^2-13y+42]/[y+2]$

Change the $\div$ $-:$ sign to $\times$ $xx$

$\frac{y + 2}{y^{2} + 2 y - 48} \times \frac{y^{2} - 13 y + 42}{y + 2}$ $[y+2]/[y^2+2y-48] xx [y^2-13y+42]/[y+2]$

factorise

$\frac{y + 2}{(y + 8) (y - 6)} \times \frac{(y - 6) (y - 7)}{y + 2}$ $[y+2]/[(y+8)(y-6)] xx [(y-6)(y-7)]/[y+2]$

cancel $(y - 6)$ $(y-6)$

$\frac{y + 2}{y + 8} \times \frac{y - 7}{y + 2}$ $[y+2]/(y+8) xx (y-7)/[y+2]$

cancel $(y + 2)$ $(y+2)$

$\frac{1}{y + 8} \times \frac{y - 7}{1}$ $1/(y+8) xx (y-7)/1$

multiply

$\frac{y - 7}{y + 8}$ $(y-7)/(y+8)$

How do you simplify y+2y2+2y−48÷y+2y2−13y+42(y+2) /(y^2+2y-48) div(y+2)/(y^2-13y+42 )?