Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ 4a-6b }{ 9 { a }^{ 8 } { b }^{ 4 } } - \frac{ 5x-4b }{ 9 { a }^{ 8 } { b }^{ 4 } }$$

Answer

$$(4*a-2*b-5*x)/(9*a^8*b^4)$$

Solution


Factor out the common term \(2\).
\[\frac{2(2a-3b)}{9{a}^{8}{b}^{4}}-\frac{5x-4b}{9{a}^{8}{b}^{4}}\]
Join the denominators.
\[\frac{2(2a-3b)-(5x-4b)}{9{a}^{8}{b}^{4}}\]
Remove parentheses.
\[\frac{2(2a-3b)-5x+4b}{9{a}^{8}{b}^{4}}\]
Expand.
\[\frac{4a-6b-5x+4b}{9{a}^{8}{b}^{4}}\]
Collect like terms.
\[\frac{4a+(-6b+4b)-5x}{9{a}^{8}{b}^{4}}\]
Simplify  \(4a+(-6b+4b)-5x\)  to  \(4a-2b-5x\).
\[\frac{4a-2b-5x}{9{a}^{8}{b}^{4}}\]
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