What is expand (-5/4 z)/(z-0.3)+(9/4 z)/(z-0.7) ?

The solution to expand (-5/4 z)/(z-0.3)+(9/4 z)/(z-0.7) is (4z^2+0.8z)/(4z^2-4z+0.84)

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expand (-5/4 z)/(z-0.3)+(9/4 z)/(z-0.7)

expand

\frac{- \frac{5}{4} z}{z - 0.3} + \frac{\frac{9}{4} z}{z - 0.7}

\frac{4 z ^{2} + 0.8 z}{4 z ^{2} - 4 z + 0.84}

Solution steps

\frac{- \frac{5}{4} z}{z - 0.3} + \frac{\frac{9}{4} z}{z - 0.7}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{5}{4} z}{z - 0.3} + \frac{\frac{9}{4} z}{z - 0.7}

\frac{\frac{9}{4} z}{z - 0.7} = \frac{9 z}{4 z - 2.8}

= - \frac{\frac{5}{4} z}{z - 0.3} + \frac{9 z}{4 z - 2.8}

Least Common Multiplier of

z - 0.3, 4 z - 2.8 : (z - 0.3) (4 z - 2.8)

Adjust Fractions based on the LCM

= - \frac{\frac{5 z ( 4 z - 2.8 )}{4}}{( z - 0.3 ) ( 4 z - 2.8 )} + \frac{9 z ( z - 0.3 )}{( 4 z - 2.8 ) ( z - 0.3 )}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- \frac{5 z ( 4 z - 2.8 )}{4} + 9 z ( z - 0.3 )}{( z - 0.3 ) ( 4 z - 2.8 )}

Convert element to a decimal form

\frac{5}{4} = 1.25

= \frac{- 1.25 z ( 4 z - 2.8 ) + 9 z ( z - 0.3 )}{( z - 0.3 ) ( 4 z - 2.8 )}

Expand

(z - 0.3) (4 z - 2.8) : 4 z^{2} - 4 z + 0.84

= \frac{- 1.25 z ( 4 z - 2.8 ) + 9 z ( z - 0.3 )}{4 z ^{2} - 4 z + 0.84}

Expand

- 1.25 z (4 z - 2.8) + 9 z (z - 0.3) : 4 z^{2} + 0.8 z

= \frac{4 z ^{2} + 0.8 z}{4 z ^{2} - 4 z + 0.84}

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What is expand (-5/4 z)/(z-0.3)+(9/4 z)/(z-0.7) ?
The solution to expand (-5/4 z)/(z-0.3)+(9/4 z)/(z-0.7) is (4z^2+0.8z)/(4z^2-4z+0.84)