Solve =3+a1/a-9/8-15/4+1/4(frac{-5}{2})

$$= 3 + \frac { a 1 } { a } - \frac { 9 } { 8 } - \frac { 15 } { 4 } + \frac { 1 } { 4 } ( \frac { - 5 } { 2 } )$$

Evaluate

$$\frac{a_{1}}{a}-\frac{5}{2}$$

Short Solution Steps

Convert 3 to fraction \frac{24}{8}.

$$\frac{24}{8}+\frac{a_{1}}{a}-\frac{9}{8}-\frac{15}{4}+\frac{1}{4}\times \frac{-5}{2}$$

Since \frac{24}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-9}{8}+\frac{a_{1}}{a}-\frac{15}{4}+\frac{1}{4}\times \frac{-5}{2}$$

Subtract 9 from 24 to get 15.

$$\frac{15}{8}+\frac{a_{1}}{a}-\frac{15}{4}+\frac{1}{4}\times \frac{-5}{2}$$

Least common multiple of 8 and 4 is 8. Convert \frac{15}{8} and \frac{15}{4} to fractions with denominator 8.

$$\frac{15}{8}+\frac{a_{1}}{a}-\frac{30}{8}+\frac{1}{4}\times \frac{-5}{2}$$

Since \frac{15}{8} and \frac{30}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-30}{8}+\frac{a_{1}}{a}+\frac{1}{4}\times \frac{-5}{2}$$

Subtract 30 from 15 to get -15.

$$-\frac{15}{8}+\frac{a_{1}}{a}+\frac{1}{4}\times \frac{-5}{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-\frac{15}{8}+\frac{a_{1}}{a}+\frac{1}{4}\left(-\frac{5}{2}\right)$$

Multiply \frac{1}{4} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{15}{8}+\frac{a_{1}}{a}+\frac{1\left(-5\right)}{4\times 2}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{4\times 2}.

$$-\frac{15}{8}+\frac{a_{1}}{a}+\frac{-5}{8}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$-\frac{15}{8}+\frac{a_{1}}{a}-\frac{5}{8}$$

Since -\frac{15}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-5}{8}+\frac{a_{1}}{a}$$

Subtract 5 from -15 to get -20.

$$\frac{-20}{8}+\frac{a_{1}}{a}$$

Reduce the fraction \frac{-20}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{5}{2}+\frac{a_{1}}{a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and a is 2a. Multiply -\frac{5}{2} times \frac{a}{a}. Multiply \frac{a_{1}}{a} times \frac{2}{2}.

$$-\frac{5a}{2a}+\frac{2a_{1}}{2a}$$

Since -\frac{5a}{2a} and \frac{2a_{1}}{2a} have the same denominator, add them by adding their numerators.

$$\frac{-5a+2a_{1}}{2a}$$

Factor

$$\frac{\frac{2a_{1}}{a}-5}{2}$$