What is 3/(2x-2)+(x+1)/4 ?

The solution to 3/(2x-2)+(x+1)/4 is (x^2+5)/(4(x-1))

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simplify 3/(2x-2)+(x+1)/4

simplify

\frac{3}{2 x - 2} + \frac{x + 1}{4}

\frac{x ^{2} + 5}{4 ( x - 1 )}

Solution steps

\frac{3}{2 x - 2} + \frac{x + 1}{4}

Least Common Multiplier of

2 x - 2, 4 : 4 (x - 1)

Adjust Fractions based on the LCM

= \frac{6}{4 ( x - 1 )} + \frac{( x + 1 ) ( x - 1 )}{4 ( x - 1 )}

Apply the fraction rule:

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

= \frac{6 + ( x + 1 ) ( x - 1 )}{4 ( x - 1 )}

Simplify

6 + (x + 1) (x - 1) : x^{2} + 5

= \frac{x ^{2} + 5}{4 ( x - 1 )}

\frac{18}{16}

(\frac{3 x ^{\frac{3}{2}} y ^{3}}{x ^{2} y ^{\frac{- 1}{2}}})^{- 2}

\frac{i ^{12} + i ^{16} - 2 i ^{18}}{i ^{8} + i ^{10}}

\frac{( 2 ^{5} ) ^{2}}{2 ^{6} \cdot 4}

(m - 6) (m^{2} + 6 m - 7)