Equations

Hong Kong

Stage 1 - Stage 3

What are the values of $A$`A` and $B$`B` that will make the equation an identity?

$\frac{1}{\left(x-6\right)\left(x+6\right)}=\frac{A}{x-6}+\frac{B}{x+6}$1(`x`−6)(`x`+6)=`A``x`−6+`B``x`+6

a

First solve for the value of $A$`A`.

b

Solve for the value of $B$`B`.

Easy

3min

What are the values of $A$`A` and $B$`B` that will make the equation an identity?

$\frac{x}{\left(x-m\right)\left(x+m\right)}=\frac{A}{x-m}+\frac{B}{x+m}$`x`(`x`−`m`)(`x`+`m`)=`A``x`−`m`+`B``x`+`m`

Easy

3min

What are the values of $A$`A` and $B$`B` that will make the equation an identity?

$\frac{3x}{\left(x+5\right)\left(x-4\right)}=\frac{A}{x+5}+\frac{B}{x-4}$3`x`(`x`+5)(`x`−4)=`A``x`+5+`B``x`−4

Medium

4min

What are the values of $A$`A` and $B$`B` that will make the equation an identity?

$\frac{x+2}{x^2}=\frac{A}{x}+\frac{B}{x^2}$`x`+2`x`2=`A``x`+`B``x`2

Hard

3min

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