{
"query": {
"display": "simplificar $$\\frac{5}{m-1}-\\frac{2}{m-3}$$",
"symbolab_question": "SIMPLIFY#simplify \\frac{5}{m-1}-\\frac{2}{m-3}"
},
"solution": {
"level": "PERFORMED",
"subject": "Algebra",
"topic": "Algebra",
"subTopic": "Simplify",
"default": "\\frac{3m-13}{(m-1)(m-3)}",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "Simplificar $$\\frac{5}{m-1}-\\frac{2}{m-3}:{\\quad}\\frac{3m-13}{\\left(m-1\\right)\\left(m-3\\right)}$$",
"input": "\\frac{5}{m-1}-\\frac{2}{m-3}",
"steps": [
{
"type": "interim",
"title": "Mínimo común múltiplo de $$m-1,\\:m-3:{\\quad}\\left(m-1\\right)\\left(m-3\\right)$$",
"input": "m-1,\\:m-3",
"steps": [
{
"type": "definition",
"title": "Mínimo común múltiplo (MCM)",
"text": "El MCM de $$a,\\:b\\:$$es el múltiplo mas pequeño que es divisible entre $$a$$ y $$b$$"
},
{
"type": "step",
"primary": "Calcular una expresión que este compuesta de factores que aparezcan tanto en $$m-1$$ o $$m-3$$",
"result": "=\\left(m-1\\right)\\left(m-3\\right)"
}
],
"meta": {
"solvingClass": "LCM",
"interimType": "LCM Top 1Eq"
}
},
{
"type": "interim",
"title": "Reescribir las fracciones basandose en el mínimo común denominador",
"steps": [
{
"type": "step",
"primary": "Multiplicar cada numerador por la misma cantidad necesaria para multiplicar el denominador correspondiente y convertirlo en el mínimo común denominador"
},
{
"type": "step",
"primary": "Para $$\\frac{5}{m-1}:\\:$$multiplicar el denominador y el numerador por $$m-3$$",
"result": "\\frac{5}{m-1}=\\frac{5\\left(m-3\\right)}{\\left(m-1\\right)\\left(m-3\\right)}=\\frac{5\\left(m-3\\right)}{\\left(m-1\\right)\\left(m-3\\right)}"
},
{
"type": "step",
"primary": "Para $$\\frac{2}{m-3}:\\:$$multiplicar el denominador y el numerador por $$m-1$$",
"result": "\\frac{2}{m-3}=\\frac{2\\left(m-1\\right)}{\\left(m-3\\right)\\left(m-1\\right)}=\\frac{2\\left(m-1\\right)}{\\left(m-1\\right)\\left(m-3\\right)}"
}
],
"meta": {
"interimType": "LCD Adjust Fractions 1Eq"
}
},
{
"type": "step",
"result": "=\\frac{5\\left(m-3\\right)}{\\left(m-1\\right)\\left(m-3\\right)}-\\frac{2\\left(m-1\\right)}{\\left(m-1\\right)\\left(m-3\\right)}"
},
{
"type": "step",
"primary": "Aplicar las propiedades de las fracciones: $$\\frac{a}{c}-\\frac{b}{c}=\\frac{a-b}{c}$$",
"result": "=\\frac{5\\left(m-3\\right)-2\\left(m-1\\right)}{\\left(m-1\\right)\\left(m-3\\right)}"
},
{
"type": "interim",
"title": "Simplificar $$5\\left(m-3\\right)-2\\left(m-1\\right):{\\quad}3m-13$$",
"input": "5\\left(m-3\\right)-2\\left(m-1\\right)",
"steps": [
{
"type": "interim",
"title": "Desarrollar $$5\\left(m-3\\right):{\\quad}5m-15$$",
"input": "5\\left(m-3\\right)",
"steps": [
{
"type": "step",
"primary": "Poner los parentesis utilizando: $$a\\left(b-c\\right)=ab-ac$$",
"secondary": [
"$$5\\left(m-3\\right)=5m-5\\cdot\\:3$$"
],
"result": "=5m-5\\cdot\\:3",
"meta": {
"practiceLink": "/practice/expansion-practice",
"practiceTopic": "Expand Rules"
}
},
{
"type": "step",
"primary": "Multiplicar los numeros: $$5\\cdot\\:3=15$$",
"result": "=5m-15"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Generic Expand Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7GNMKNOPqVJrXiIPh3rQ6ewsBmUOGgB0VAXoAXik9qC9EoApuujwRq/Ms3wa4gNT89ZVSO0B13oSpK+zJfqv7kFQkXX4bZTTEXIY5gc0SycL45bas9TEXDWczAbcj2/yBsIjaxJ4DvjTb2fbKjbvtlQ=="
}
},
{
"type": "step",
"result": "=5m-15-2\\left(m-1\\right)"
},
{
"type": "interim",
"title": "Desarrollar $$-2\\left(m-1\\right):{\\quad}-2m+2$$",
"input": "-2\\left(m-1\\right)",
"steps": [
{
"type": "step",
"primary": "Poner los parentesis utilizando: $$a\\left(b-c\\right)=ab-ac$$",
"secondary": [
"$$-2\\left(m-1\\right)=-2m-\\left(-2\\right)\\cdot\\:1$$"
],
"result": "=-2m-\\left(-2\\right)\\cdot\\:1",
"meta": {
"practiceLink": "/practice/expansion-practice",
"practiceTopic": "Expand Rules"
}
},
{
"type": "interim",
"title": "$$-\\left(-2\\right)\\cdot\\:1=2$$",
"input": "-\\left(-2\\right)\\cdot\\:1",
"steps": [
{
"type": "step",
"primary": "Aplicar la propiedad: $$-\\left(-a\\right)=a$$",
"secondary": [
"$$-\\left(-2\\right)=2$$"
],
"result": "=2\\cdot\\:1"
},
{
"type": "step",
"primary": "Multiplicar los numeros: $$2\\cdot\\:1=2$$",
"result": "=2"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Solver2",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7zA1dH5zWL1siW/PXCNQxai061ljBSPJeENOw2efoSWt8rNweSBKaNqhWM5iGGSVMMb1QS31aBvYHwKLXjUkAb3lP9vXoXSyY9eaysz9yDlg="
}
},
{
"type": "step",
"result": "=-2m+2"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Generic Expand Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7kI5yzuMMD9CbUkSPAp272HcUJadsLvGcDY7IUPYXjf6zs903yhxK0NInTwR7JvSRyM/29l7SHlwNleTQoRn0qGbU+JSSzhwT4U9vUdKov1SBcomBG73YMaTPbYTFf9X1YcTfc1m1XpAfMZNyVDp9Wg=="
}
},
{
"type": "step",
"result": "=5m-15-2m+2"
},
{
"type": "interim",
"title": "Simplificar $$5m-15-2m+2:{\\quad}3m-13$$",
"input": "5m-15-2m+2",
"steps": [
{
"type": "step",
"primary": "Agrupar términos semejantes",
"result": "=5m-2m-15+2"
},
{
"type": "step",
"primary": "Sumar elementos similares: $$5m-2m=3m$$",
"result": "=3m-15+2"
},
{
"type": "step",
"primary": "Sumar: $$-15+2=-13$$",
"result": "=3m-13"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7SM58qNN4+ObYFUGgiwqqJSAn9lkDfZkicUGkO3EF+IoMYu+sRrm2PHcz2KiorrPPo3oe/oyhMy2+1TQhDBd2f5puUz+FjAD3TNWs+NNmoGJNEwO9+2/tSuc++thwKP4oJLd1ohke2Wgml78++2zI0g=="
}
},
{
"type": "step",
"result": "=3m-13"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7OoFITXqmTqi3MH+QMc3vRS061ljBSPJeENOw2efoSWtbzA/qN7RDXwVwFsb/E2pHLFkLZJTec9/y4HD02wKt2XKF3u2OIb4bFA3EO8aRlSVmVAF6G4zVWKKcSbzqy+/zvCZID4DeTLvIfZPyitd4kw=="
}
},
{
"type": "step",
"result": "=\\frac{3m-13}{\\left(m-1\\right)\\left(m-3\\right)}"
}
],
"meta": {
"solvingClass": "Solver2"
}
},
"meta": {
"showVerify": true
}
}
Solución
simplificar
Solución
Pasos de solución
Mínimo común múltiplo de
Reescribir las fracciones basandose en el mínimo común denominador
Aplicar las propiedades de las fracciones:
Simplificar