Reoxidation of cytosolic NADH:

The inner mitochondrial membrane is impermeable to NADH. Thus NADH generates in the cytoplasm in during glycolysis must be reoxidized through a membrane shuttle and a combination   of enzyme reactions which bypass this impermeability barrier. In the figure shows the glycerol 3-phosphate shuttle. The Dihydroxyacetone phosphate in the cytosol is decreased to glycerol 3-phosphate and NADH reoxidized to NAD⁺, through cytosolic glycerol 3-phosphate dehydrogenase.  A glycerol 3-phosphate diffuses across the inner mitochondrial membrane where it is transformed back to dihydroxyacetone phosphate through mitochondrial glycerol 3-phosphate dehydrogenase and a transmembrane protein of the inner mitochondrial membrane. A dihydroxyacetone phosphate then diffuses back to the cytosol.  A mitochondrial glycerol 3-phosphate dehydrogenase does not use NAD⁺ but in alternate uses FAD. The enzyme-linked FADH₂ (E.FADH₂) is then reoxidized through transferring its electrons to ubiquinone in the similar inner mitochondrial membrane. Note that the shuttle does not permit cytoplasmic NADH to enter the mitochondrion  but  its  operation  efficiently  transports  the  two  electrons  from  the NADH into the mitochondrion  and feeds them into the electron transport chain.

Figure:  The glycerol 3-phosphate shuttle.

Because the electrons from cytoplasmic NADH originally enter the electron transport chain from FADH₂, only about two ATPs are synthesized instead of around three ATPs from each NADH which arises inside the mitochondrion from the citric acid cycle and fatty acid oxidation.

A same shuttle, the malate-aspartate shuttle, operates in liver and heart. Oxaloacetate in the cytosol is transformed to malate through cytoplasmic malate dehydrogenase, reoxidizing NADH to NAD⁺ in the procedure.  The malate enters the mitochondrion through a malate-α-ketoglutarate carrier in the inner mitochondrial membrane. In this matrix the malate is reoxidized to oxaloacetate through NAD to form NADH.  The Oxaloacetate   does  not  simply  cross  the  inner  mitochondrial membrane  and so is transaminated  to form aspartate that then exits from the mitochondrion   and  is  reconverted   to  oxaloacetate   in  the  cytosol,  again  through transamination.  The total result of this cycle of reactions is to transfer the electrons from NADH in the cytosol to NADH in the mitochondrial matrix that is then reoxidized through the electron transport chain.

Figure: The malate-aspartate shuttle.