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\[\frac{ 5b+10 }{ a } *\frac{ a }{ 5b-15}\]
\[\frac{ 3x+21 }{ 8x } / \frac{ 3 }{ 2x }\]
factor, cancel \[\frac{5b+10}{a}\times \frac{a}{5b-15}=\frac{5(b+2)\times a}{a\times 5(b-3)}\] \[=\frac{\cancel 5(b+2)\cancel a}{\cancel a\cancel 5(b-3)}=\frac{b+2}{b-3}\]
\[\frac{\frac{3x+21}{8x}}{\frac{3}{2x}}\] multiply by the reciprocal (just like with numbers) \[=\frac{3x+21}{8x}\times \frac{2x}{3}\]
then factor and cancel \[\frac{3(x+7)\times 2x}{3\times 8x}=\frac{\cancel 3(x-7)\cancel {2x}}{\cancel 3\cancel {8x}}=\frac{x-7}{4}\]
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oops typo there, should be \[\frac{x+7}{4}\]
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